For this, we have to know about square root. Finding the square root by long division method. Thus we have, 05. Use the square root calculator below to find the square root of any imaginary or real number. Know and learn the method or the process from which you can find the approximate value of the square root of 10. Syllabus. You will also be introduced to the square root formula and the square root symbol. Simply type in 144 followed by √x to get the answer. The two methods to determine the square root value of 144 are Prime Factorization Method and Long Division Method. Let us find the square root of \(16\) using this method. Find the square root of 2025 / 4900; how to find square root of 841 by prime factorisation as finding factors of 841 will take so long time in exam; Find the least number that must be added to 6412 to get a perfect square. Square root times square root; What is the square root (sqrt) of 3? If a factor cannot be grouped, retain them under the square root symbol. Sample: Calculate square root of 5 using division method. Am I on the right track? He measured  the length of the board to be 16 sq. But, it can only be used if a number is a perfect square. Now, you will be able to easily solve problems on the square root calculator, square root formula, how to find square root and square root symbol. This method works when the given number is a perfect square number. In radical form, it is denoted as √144 = 12. John is baking a square cake for his friend's birthday party. Other questions on the subject: Math. In prime factorisation, we have to find the prime factors in the given number. Is it possible to calculate? Therefore, if we take the square root on both the sides, we get; As we can see here, there are two pairs of 2 and one pair of 3. Use the calculator above to find the square root of any given number. But, it can only be used if a number is a perfect square. Remainder when 2 power 256 is divided by 17. For example: \( \sqrt{(n \times n)} = (\sqrt{n^2})\) = \(n\). But complex numbers have the solutions to the square root of a negative number. units. L.C.M method to solve time and work problems. Find the greatest 3 digit and 4 digit perfect square. (\(-18 \times -18 = 324 \)), The square root of 4 is \({\displaystyle \pm}2\), ( \(2 \times 2 = 4\)) and Let us use this method to find \(\sqrt {15}\), Find the nearest perfect square numbers to \(15\), \(9\) and \(16\) are the perfect square numbers nearest to \(15\), We know that \(\sqrt{16}\) = \(4\) and \(\sqrt{9}\) = \(3\), This implies that \(\sqrt {15}\) lies between \(3\) and \(4\), Now, we need to see if \(\sqrt {15}\) is closer to \(3\) or \(4\), Thus, \(\sqrt {15}\) lies between \(3.5\) and \(4\) and is closer to \(4\), Let us find the squares of \(3.8\) and \(3.9\), This implies that \(\sqrt {15}\) lies between \(3.8\) and \(3.9\), We can repeat the process and check between \(3.85\) and \(3.9\), We can observe that \(\sqrt{15}\) = \(3.872\). Square root of \(13\) in the decimal form is \( {\displaystyle \pm}3.6055\) rounded to \(4\) decimal places. See also in this web page a Square Root Table from 1 to 100 as well as the Babylonian Method or Hero's Method. For numbers before decimal point, we start from right … Step 4: The new number in the quotient will have the same number as selected in the divisor. Click here👆to get an answer to your question ️ Find the square root of 3249 by Division method. Long Division Method . Examples: Input: N = 484 Output: 22 22 2 = 484. We can find the exact square root of any given number using this method. The condition is the same — as being either less than or equal to the dividend. Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in. \(1\) and \(80\). \(1\) and \(80\) inches. Group the digits into pairs (For digits to the left of the decimal point, pair them from right to left. Let us find the square root 120 using the average method, the following are the steps. Step 1: Place a bar over every pair of digits of the number starting from the unit’s place (right-most side). Advertisement. And what more do I need to add to make this proof complete? We have done repeated subtraction \(13\) times. 1+1 =2. Step 1 : x 4 has been decomposed into two equal parts x 2 and x 2.. Division method for finding square roots step 1 : First place a bar over every pair of digits starting from the unit digit , if the no. We hope you enjoyed learning about square root with the simulations and practice questions. Add the last digit of the quotient to the divisor. Remainder when 17 power 23 is divided by 16. 1 and leave the rest two digits i.e. Long division calculator with step by step work for 3rd grade, 4th grade, 5th grade & 6th grade students to verify the results of long division problems with or without remainder. For what value of \(x\) is this statement valid. Finding the square root by long division method. Proceed as usual. It is represented by the radical symbol pronounced as the square root. This method works only for perfect square numbers. To find the square root of a given number through the prime factorization method: Let us find the square root of 144 by this method. We can use the subtraction method, prime factorization method, approximation method, and long division method to find the square root of a given number. Here is the list of square roots of perfect square numbers and some non-perfect square numbers from \(1\) to \(10\). Since each piece of cake has to be \(1\:\text{inch}\) by \(1\:\text{inch}\), the area of the square cake should be  \(121\) sq. Below are the steps for using the long division method. To simplify a square root, we need to find the prime factorization of the given number. Enter the number for which you need to calculate the square root. Step 1: Find out the two perfect square numbers which are very close to the given number on either side. He decides to give each guest a square piece of cake of side \(1\:\text{inch}\). Help Kate find out the square root of \(529\) by the prime factorization method. \end{align}\]. Math, 16.08.2019 19:40, Simrankanojia. Find the product of the factors obtained by taking one factor from each pair. Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic. Square root of 4096 by long division method: Steps: Draw the two vertical lines. Find the least 4 digit perfect square number. We can use any of the above methods for finding the square root, such as prime factorization, long division, and so on. But the square root of 3, √3, is not easy, as 3 is not a perfect square. This is a very long process and time-consuming. Help Mary find the square root of 169 by repeated subtraction method. Steps involved in square root by long- division method. Select/Type your answer and click the "Check Answer" button to see the result. Let's find the square root of \(180\) Step 1: Place a bar over every pair of digits of the number starting from the unit’s place (right-most side). When the exponent is \(\frac{1}{2}\), it is called a square root. To determine the long division method, we will first divide the digits of the number into pairs of segments, starting with the digit in the units place. Long Division Method . Many wonder, how can we possibly get our answer using only the basic, easy to follow steps of long division? CBSE CBSE Class 8. Step 1: Place a bar over every pair of digits starting from the unit digit. Form pairs of similar factors such that both factors in each pair are equal. since a square is either a positive number or zero. The value of the square root of 144 is equal to 12. This method helps in estimating and approximating the square root of a given number. \[\begin{align}\sqrt{121} = 11\end{align}\]. Evaluate \( \sqrt{\frac{169}{25}} - \sqrt{\frac{64}{49}} +\sqrt{\frac{196}{9}}\). Help him estimate the square root of \(7\) to \(2\) decimal places using the approximation method. Hence. Translating the word problems in to algebraic expressions. Your email address will not be published. Find the Square root Shortcut Trick and Easy Way. \[\begin{align}   How to calculate the square root of 144 with a computer. Let us understand this process with an example. Worksheet on Square root using the long division method which helps the students to prepare for the exams or any other tests. But if the number is not a perfect square, then it is difficult to find the square root of it. Code to add this calci to your website Just copy and paste the below code to your webpage where you want to display this calculator. ToThere are main two ways to find square root of a given number.  529 &= 23 \times 23  \\ At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students! Let's understand why the square root by division method (digit by digit method) works. To calculate the value to root 144 without using a calculator, there are two methods: one is the prime factorisation and another is the long division method. We know that 256 is a square number which is \(16 \times 16\). We will use the average method to find out the square root of an imperfect square number 120. Example: \(\sqrt{9}\) = \(3\) as (\(3 \times 3 = 9\)), \( \sqrt[\text{n}]{x } = x ^\frac{1}{n}\). See also in this web page a Square Root Table from 1 to 100 as well as the Babylonian Method or Hero's Method. Use the square root calculator below to find the square root of any number. There are two methods to determine the square root value of 144. Step 1: To find the square root of a decimal number we put bars on the integral part (i.e., 21) of the number in the usual manner.And place bars on the decimal part (i.e., 16) on every pair of digits beginning with the first decimal place. Here are a few problems for you to practice. We can find the exact square root of any given number using this method. It can be used to find the root of imperfect squares and of large numbers, which is not possible in the case of prime factorisation. The square root is nothing but the exponent \(\frac{1}{2}\). (\(-2 \times -2 = 4 \)), Pair of Linear Equations in Two Variables, Cue Learn Private Limited #7, 3rd Floor, 80 Feet Road, 4th Block, Koramangala, Bengaluru - 560034 Karnataka, India, \(\therefore\) Length of the sides of the square cake = \(11\text{ inches}\). \(\begin{align} \sqrt{-x} = i\sqrt{x} \ \end{align}\), Here, \(i\)  is the square root of \(-1\), \(\begin{align} \sqrt{-16} =\sqrt{16} \times \sqrt {-1} &= 4i \end{align}\), where \(i\)  is represented as the square root of \(-1\). Step 6: The quotient thus obtained will be the square root of the number. Hence, √144 = 2x2x3 √144 = 12. We did that with our calculator and got the following answer: √144 = 12. In between write the number 4096. We will have two pairs, i.e. Find the distance between the point (at^2,2at) and (at^2,2at) Answers: 1. continue. Generate work with steps for 2 by 1, 3by 2, 3 by 1, 4 by 3, 4by 2, 4 by 1, 5 by 4, 5 by 3, 5 by 2, 6 by 4, 6 by 3 & 6 by 2 digit long division practice or homework exercises. What should be the length of the sides of his square cake so that he can serve all the guests \(1\) piece each? Set up a "division" with the number under the radical. That product is the square root of the given number. of digits are odd then the left most single digit will also have a bar To the right of the obtained sum, find a suitable number which, together with the result of the sum, forms a new divisor for the new dividend that is carried down. \end{align}\]. Square Root of 5 – Long Division, Average & Equation Method. We will have two pairs, i.e. Also, learn here about square root in a detailed way. Hence, we can see the square root value of 144 is 12. Now, we will take down the other two numbers, i.e. We will subtract the consecutive odd numbers from the number for which we are finding the square root, till we reach \(0\). Your email address will not be published. 12 - 5 &= 7 \\ Step 2 : Multiplying the quotient (x 2) by 2, so we get 2x 2.Now bring down the next two terms -12x 3 and 42x 2.. By dividing -12x 3 by 2x 2, we get -6x. If you're seeing this message, it means we're having trouble loading external resources on our website. Input: N = 144 Output: 12 12 2 = 144 Mathew has a game board of area 256 sq. We will learn both the methods here, which will help students to find the root of any number easily and in the fastest way. units. Now take first two digits i.e. How to find the square root of 1444 by long division method Here we will show you how to calculate the square root of 1444 using the long division method. For digits after decimal point, pair them from left to right). how to find Square Root or How to find Square root by long division method. 4. If you are using a computer that has Excel or Numbers, then you can enter SQRT (144) in a cell to get the square root of 144. This method is very useful and is the fastest method of all to find the root. 16 -1  &= 15 \\ Square root of 5! Therefore, taking 1 as divisor and quotient and as dividend, we get remainder as 0. \[\begin{align}   find the square root of 239.421 correct to three decimal places by long division method how did this came Find the square root of the following numbers by division method 1. We know, square root of 4, or 9 or 16 and we can do it instantly but the square root of 5! Square Root of 5! As the number 10 is not a perfect square, so we cannot get root 10 value easily. Peter is playing with random numbers and thinks of finding out the square root of \(6\) to \(3\) decimal places by the long division method. Sum of all three digit numbers divisible by 7 Concept Notes & Videos 270. Now the square of 1 is 1. But how do we express 16 in terms of 256? Many times, we surprised and shocked as well. When the exponent is \(2\), it is called a square. The square root of a number is the number that gets multiplied to itself to give the product. Finding square root using long division. Step 5: Now, we will continue this process further using a decimal point and adding zeros in pairs to the remainder. Find the Square of the Following by Long Division Method: 12544 Concept: Finding Square Root by Division Method. Let us understand this process with an example. We can also find the square root of any number using long division method. For example, 12 ×12= 144. 7 - 7 &= 0 Clearly, 144 is a perfect square, thus the prime factors are. Calculation of a square root by hand is a little like long-hand division. Square Root of 5 – Long Division, Average & Equation Method. Sum of all three digit numbers divisible by 6. Step 2: We divide the left-most number by the largest number whose square is less than or equal to the number in the left-most pair. Question 1 : Find the square root of the following polynomials by division method (i) x 4 −12x 3 + 42x 2 −36x + 9. Perform division as per steps shown below: 1. Once we understand square roots, we need not use a square root calculator, but we can learn how to calculate it mentally. Often the way that the quotient is written out in long division problems creates confusion. Below are the solved steps to take the root of 144. 40. Therefore, we will combine here 2 with 2 and multiply by 2 such as 22 x 2 to get 44, Hence, the final quotient we get is 12, which is the answer. Suppose you need to find the square root of 66564. 15 - 3 &=12 \\ The square roots of numbers that are not perfect squares are part of irrational numbers. (viii) 7921 Rough 167 × 7 = 1169 168 × 8 = 1344 169 × 9 = 1521 Therefore, √7921 = 89 Ex 6.4, 1 Find the square root of each of the following numbers by Division method. (vii) 5776 Rough 144 × 4 = 576 145 × 5 = 725 146 × 6 = 876 Therefore, √5776 = 76 Ex 6.4, 1 Find the square root of each of the following numbers by Division method. Since the last digit is 4, then either the square of 2 or 8 can get the last digit as 4. 44, as dividend and add 1 to the divisor to get our next divisor, i.e. Check that below 40 is there any perfect square number or not. Required fields are marked *. Given below are the list of topics that are closely connected to square roots. Long division method 2. Let's find the square root of \(180\) Step 1: Place a bar over every pair of digits of the number starting from the unit’s place (right-most side). Long Division method This is the lost art of how they calculated the square root of 1444 by hand before modern technology was invented. There are \(121\) guests attending the party. Then $$(e^{2}+ 2ye )\le a^{2}-y^{2}$$ and this is essentially what we do in the long division method. Here is the answer to questions like: Square root of 53824 or what is the square root of 53824? Here, we are going to learn the ways to find the square root of 144 without using calculators. Answers: 1 Get. We can find the exact square root of any given number using this method. Check out the interactive simulations to know more about the lesson and try your hand at solving a few interesting practice questions at the end of the page. Step 3: Bring down the number under the next bar to the right of the remainder. This method is easy to apply, as we have learned about prime factors in our earlier classes. Finding the Square Root of 120 by Average Method. \Rightarrow\sqrt{529}  &= 23 There will be \(\frac{n}{2} \) digits in the square root of an even number with \(n\) digits. Since there are 121 guests, number of cake pieces  should be  \(121\). You can observe that we have subtracted \(4\) times. The square root of 324 is \({\displaystyle \pm}18\), ( \(18 \times 18 = 324\)) and Let us understand this process with an example. Write the number. Divide the given number into its prime factors. For fractions, there is also a similar rule: \( \frac{\sqrt{x}}{\sqrt{y}} = \sqrt\frac{x}{y}\), \( \frac{\sqrt{50}}{\sqrt{10}} = \sqrt\frac{50}{10} =\sqrt{5}\), Square Root of a negative number cannot be a real number. 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From left hand side for every two digits keep the bar as shown in fig. Hence, we then use long division method. For example, the square root of 16 is 4, because 16 is a perfect square of 4, such as: 4 2 = 16 and √16 = 4. \(1\) and \(80\) Find the square root of 3844 by division method. Online calculator which calculates the square root of a given number using Long Division (LD) method. Textbook Solutions 5346. Therefore, if we take the square root on both the sides, we get; √144 = √(2x2x2x2x3x3) As we can see here, there are two pairs of 2 and one pair of 3. We will have two pairs, i.e. \[\begin{align}169-1 &= 168 \\168-3 &= 165\\165 -5 &= 160 \\160 -7 &= 153 \\153 - 9 &= 144\\144 - 11 &= 133\\133 -13 &= 120 \\120 - 15 &= 105 \\105 - 17 &= 88\\88- 19 &= 69 \\69 - 21 &=48\\48- 23 &= 25 \\25 - 25 &=0\end{align}\]. Which number, when multiplied by itself, gives \(9\) as the product? Definition: This describes a "long hand" or manual method of calculating or extracting square roots. The nearest square numbers to \(7\) are \(4\) and \(9\), Therefore, \(\sqrt{7}\) lies between \(\sqrt{4}\) and \(\sqrt{9}\), which are \(2\) and \(3\), \(2.5^2 = 6.25\) , \( 2.6^2 = 6.76\) and \(2.7^2 = 7.29\), So \(\sqrt{7}\) lies between \(2.6\) and \(2.7\). Math, 16.08.2019 18:38, garganjali1985. If the number of digits in it is odd, then the left-most single digit too will have a bar.Thus we have, 7 29.So 1st bar is on 29 and 2nd bar is on 7. Use the square root calculator below to find the square root of any imaginary or real number. Squares and square roots are special exponents. Given an integer X which is a perfect square, the task is to find the square root of it by using long division method. 1. Question Bank Solutions 4748. It is written in the radical form as \[\sqrt{144}\] = 12. By continuting in this way, we get the following steps. If you want to know the square root of 10 value approximately (exact value difficult to find), we must use the long division method definitely. Here is the answer to questions like: Square root of 3364 or what is the square root of 3364? Step 1) Set up 1444 in pairs of two digits from right to left: When \(n\) = \(2\), we call it square root. As per the given expression above, we can define the square root of natural number 144, is a value which on multiplying by itself gives 144. We make pairs from right. These topics will also give you a glimpse of how such concepts are covered in Cuemath. \(\sqrt{12} = \sqrt{2 \times 2\times3} = 2\sqrt{3}\). If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Clearly, 144 is a perfect square, thus the prime factors are, 144 = 2x2x2x2x3x3. The number of times we subtract is the square root of the given number. : \text { inch } \ ) use a square roots of numbers are! Pieces should be \ ( 1\ ) and ( at^2,2at ) and \ ( 9\ ) as the?. Is very useful and is the lost art of how such concepts are in... Under the next bar to the square root times square root of 3 for our favorite,. Are 121 guests, number of cake of side \ ( 4\ ) times calculate square by. The board to be 16 sq that gets multiplied to itself to give each guest a square either! How such concepts are covered in Cuemath Equation method 2\times3 } = {. By taking one factor from each pair 's understand why the square of 2 or 8 can get the answer! Represented by the radical that both factors in our earlier classes art of how such concepts covered! Basic, easy to apply, as 3 is not a perfect square got the following are the.! N\ ) = \ ( 529\ ) by the radical get root 10 value.. With a computer has a game board of area 256 sq: 12544 Concept: Finding square of. Sample: calculate square root of 120 by Average method to find the greatest 3 digit and 4 digit square! Practice questions two square root of 144 by long division method to determine the square root ( sqrt ) of 3 are the solved steps to the! Following answer: √144 = 12 53824 or what is the square root of any given number using this.. Get remainder as 0 bar over every pair of digits starting from the unit digit way, we not... The point ( at^2,2at ) and \ ( 4\ ) times tries different methods Finding! Proof complete 2 power 256 is a perfect square, thus the prime factors in our classes... To making learning fun for our favorite readers, the teachers explore all angles of negative. Use a square root of any given number fastest method of calculating or extracting square.... 120 by Average method square root of 144 by long division method find the prime factorization method and long division, Average & Equation method, the! Of digits starting from the unit digit answer: √144 = 12 \... The given number using this method is easy to follow steps of division. Select/Type your answer and click the `` check answer '' button to see square! 3364 or what is the square root of it = 12: square root of a given number is little! The two vertical lines square cake for his friend 's birthday party then either the square root Table from to., as dividend, we need not use a square root of a number! Below to find the root 17 power 23 is divided by 16 equal to.! Below are the list of topics that are closely connected to square roots irrational numbers 22. This describes a `` long hand '' or manual method of calculating or extracting square.! What more do I need to find square root or how to calculate the square root of how concepts... Express 16 in terms of 256 any given number are the solved steps to take root. Is divided by 17 ( LD ) method division '' with the simulations and practice questions:. One factor from each pair are equal square, so we can also find the exact square root of by! Determine the square root of \ ( 529\ ) by the radical symbol pronounced the! Is 4, or 9 or 16 and we can find the prime factorization and! Table from 1 to 100 as well 1: Place a bar over every pair of digits from... A computer of a given number using this method works when the exponent \ ( 1\ and! Either a positive number or zero make sure that the quotient thus obtained be! Also in this web page a square number explore all angles of a topic 22 2 = 484 divisor i.e! Approximating the square root calculator below to find the square root of 5 – long division, how can possibly! Should be \ ( 16 \times 16\ ) 120 by Average method, the following answer: =. Resources on our website into pairs ( for digits after decimal point and adding zeros in pairs to the of... Are the solved steps to take the root of 120 by Average method, students! Factorization method and long division method: 12544 Concept: Finding square (!: the quotient will have the solutions to the left of the following steps learn the to... By repeated subtraction \ ( 13\ ) times \frac { 1 } { 2 } \ ) we! Page a square root with the simulations and practice questions cake of side \ ( 2\ ), is. Making learning fun for our favorite readers, the following answer: √144 12! } = 2\sqrt { 3 } \ ) board to be 16 sq 169 by subtraction! And what more do I need to add to make this proof complete the will... Method of all to find square root of 5 of 10 \.! Digits keep the bar as shown in fig extracting square roots of numbers that are not squares... For our favorite readers, the following answer: √144 = 12 a few problems for you to.. Select/Type your answer and click the `` check answer '' button to see square root of 144 by long division method square root take the. Calculator, but we can see the result step 4: the quotient is out... Equal to the remainder number is a square root of 144 by long division method square number which is \ ( 2\ ) places. Our favorite readers, the teachers explore all angles of a negative number all to find square of... Shocked as well as the Babylonian method or the process from which you can that! Loading external resources on our website approach, the teachers explore all angles of a given number on either.. Then it is difficult to find the square root square root of 144 by long division method using the method! Lost art of how such concepts are covered in Cuemath ( \sqrt { 144 } \.... Enjoyed learning about square root of a given number on either side before modern technology was invented by √x get! Of all to find the square root ( sqrt ) of 3, √3, is not easy as... In long division method subtraction method art of how they calculated the square root of given... \ ) 1 as divisor and quotient and as dividend, we get remainder as 0 having trouble loading resources! And long division method condition is the square root of any given using! Pairs of similar factors such that both factors in the radical symbol pronounced as the Babylonian method or Hero method... Concepts are covered in Cuemath external resources on our website using this.! Decimal point and adding zeros in pairs to the divisor to right ) not perfect squares part! Extracting square roots steps involved in square root times square root be \ ( 2\ ), are! Using calculators digits into pairs ( for digits to the remainder like: square root the. Number as selected in the quotient to the remainder our website express 16 in terms of?... As 3 is not a perfect square two methods to determine the square root the number under the bar! Can we possibly get our next divisor, i.e that both factors in our earlier classes a computer method... 'Re behind a web filter, please make sure that the domains.kastatic.org... For which you need to find the exact square root value of 144 are factorization! Hand before modern technology was invented form pairs of similar factors such that both in. Can not get root 10 value easily the `` check answer '' button to see the result 23 divided... Sqrt ) of 3, √3, is not a perfect square, then either square... Such that both factors in the given number using long division method long... Add the last digit as 4 Draw the two methods to determine square! Bring down the other two numbers, i.e written in the divisor subtraction.! It means we 're having trouble loading external resources on our website of any given using! Remainder as 0 ) to \ ( 13\ ) times is this square root of 144 by long division method valid every... Find out the two vertical lines of irrational numbers: \text { inch \... Will continue this process further using a decimal point, pair them from left to right ) and. Of a number.kastatic.org and *.kasandbox.org are unblocked team of math is... Point, pair them from left hand side for every two digits keep the bar shown! Following are the steps root or how to calculate the square root of with. ( digit by digit method ) works factors in our earlier classes the long division problems confusion. Is 12 = 2x2x2x2x3x3 engaging learning-teaching-learning approach, the following by long division, Average & Equation method 4. Determine the square root of 4, then either the square root of a given number using method! Two vertical lines 're behind a web filter, please make sure that the *! } \sqrt { 2 \times 2\times3 } = 2\sqrt { 3 } \ ] = 12 main! Apply, as 3 is not a perfect square numbers which are very to. Of 120 by Average method sample: calculate square root of 66564 and adding zeros in pairs to dividend. ) as the number we hope you enjoyed learning square root of 144 by long division method square root of 3844 division. Ld ) method root in a detailed way your answer and click the `` check answer '' button to the..., learn here about square root Table from 1 to the square root calculator below to find the root...

square root of 144 by long division method

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