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2026-01-01
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2026-02-28
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<p>229 Learners</p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1072.</p>
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<h2>What is the Square Root of 1072?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 1072 is not a<a>perfect square</a>. The square root of 1072 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1072, whereas (1072)^(1/2) in the exponential form. √1072 ≈ 32.7405, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<h2>Finding the Square Root of 1072</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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<ul><li>Prime factorization method </li>
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<li>Long division method</li>
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<li>Approximation method</li>
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</ul><h2>Square Root of 1072 by Prime Factorization Method</h2>
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<p>The<a>product</a>of prime<a>factors</a>is the Prime factorization of a number. Now let us look at how 1072 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1072 Breaking it down, we get 2 x 2 x 2 x 2 x 67: 2^4 x 67</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1072. The second step is to make pairs of those prime factors. Since 1072 is not a perfect square, the digits of the number can’t be grouped in pairs perfectly.</p>
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<p>Therefore, calculating 1072 using prime factorization is complicated.</p>
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<h2>Square Root of 1072 by Long Division Method</h2>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step:</p>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step:</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1072, we need to group it as 72 and 10.</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1072, we need to group it as 72 and 10.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 10. We can say n as ‘3’ because 3 x 3 = 9 is less than 10. Now the<a>quotient</a>is 3, and after subtracting 10 - 9, the<a>remainder</a>is 1.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 10. We can say n as ‘3’ because 3 x 3 = 9 is less than 10. Now the<a>quotient</a>is 3, and after subtracting 10 - 9, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Now let us bring down 72, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 3 + 3 = 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 72, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 3 + 3 = 6, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor is 6n. We need to find the value of n such that 6n x n ≤ 172. Let us consider n as 2, now 62 x 2 = 124.</p>
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<p><strong>Step 4:</strong>The new divisor is 6n. We need to find the value of n such that 6n x n ≤ 172. Let us consider n as 2, now 62 x 2 = 124.</p>
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<p><strong>Step 5:</strong>Subtract 124 from 172; the difference is 48, and the quotient is 32.</p>
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<p><strong>Step 5:</strong>Subtract 124 from 172; the difference is 48, and the quotient is 32.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4800.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4800.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which is 649 because 649 x 7 = 4543.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which is 649 because 649 x 7 = 4543.</p>
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<p><strong>Step 8:</strong>Subtracting 4543 from 4800, we get the result 257.</p>
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<p><strong>Step 8:</strong>Subtracting 4543 from 4800, we get the result 257.</p>
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<p><strong>Step 9:</strong>Now the quotient is 32.7.</p>
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<p><strong>Step 9:</strong>Now the quotient is 32.7.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero.</p>
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<p>So the square root of √1072 is approximately 32.74.</p>
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<p>So the square root of √1072 is approximately 32.74.</p>
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<h2>Square Root of 1072 by Approximation Method</h2>
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<p>The approximation method is another method for finding the square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 1072 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √1072. The smallest perfect square less than 1072 is 1024, and the largest perfect square<a>greater than</a>1072 is 1089. √1072 falls somewhere between 32 and 33.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula: (1072 - 1024) / (1089 - 1024) = 48 / 65 ≈ 0.738 Using the formula, we identified the<a>decimal</a>point of our square root. The next step is adding the value we got initially to the decimal number, which is 32 + 0.738 ≈ 32.74.</p>
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<p>So the square root of 1072 is approximately 32.74.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1072</h2>
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<p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in long division methods. Now let us look at a few of these mistakes in detail.</p>
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<h3>Problem 1</h3>
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<p>Can you help Max find the area of a square box if its side length is given as √1072?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is 1072 square units.</p>
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<h3>Explanation</h3>
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<p>The area of the square = side^2.</p>
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<p>The side length is given as √1072.</p>
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<p>Area of the square = side^2</p>
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<p>= √1072 x √1072</p>
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<p>= 1072.</p>
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<p>Therefore, the area of the square box is 1072 square units.</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<p>A square-shaped building measuring 1072 square feet is built; if each of the sides is √1072, what will be the square feet of half of the building?</p>
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<p>Okay, lets begin</p>
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<p>536 square feet</p>
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<h3>Explanation</h3>
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<p>We can just divide the given area by 2 as the building is square-shaped.</p>
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<p>Dividing 1072 by 2, we get 536.</p>
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<p>So half of the building measures 536 square feet.</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<p>Calculate √1072 x 5.</p>
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<p>Okay, lets begin</p>
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<p>163.7025</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 1072, which is approximately 32.7405.</p>
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<p>The second step is to multiply 32.7405 by 5.</p>
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<p>So, 32.7405 x 5 ≈ 163.7025.</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<p>What will be the square root of (1024 + 48)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is 33.</p>
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<h3>Explanation</h3>
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<p>To find the square root, we need to find the sum of (1024 + 48).</p>
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<p>1024 + 48 = 1072, and then √1072 ≈ 32.74.</p>
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<p>Therefore, the square root of (1024 + 48) is approximately ±32.74.</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √1072 units and the width ‘w’ is 38 units.</p>
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<p>Okay, lets begin</p>
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<p>The perimeter of the rectangle is approximately 141.48 units.</p>
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<h3>Explanation</h3>
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<p>Perimeter of the rectangle = 2 × (length + width).</p>
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<p>Perimeter = 2 × (√1072 + 38)</p>
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<p>≈ 2 × (32.7405 + 38)</p>
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<p>= 2 × 70.7405</p>
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<p>≈ 141.48 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 1072</h2>
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<h3>1.What is √1072 in its simplest form?</h3>
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<p>The prime factorization of 1072 is 2 x 2 x 2 x 2 x 67, so the simplest form of √1072 = √(2^4 x 67).</p>
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<h3>2.Mention the factors of 1072.</h3>
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<p>Factors of 1072 are 1, 2, 4, 8, 16, 67, 134, 268, 536, and 1072.</p>
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<h3>3.Calculate the square of 1072.</h3>
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<p>We get the square of 1072 by multiplying the number by itself, that is, 1072 x 1072 = 1,149,184.</p>
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<h3>4.Is 1072 a prime number?</h3>
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<p>1072 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1072 is divisible by?</h3>
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<p>1072 has several factors; these are 1, 2, 4, 8, 16, 67, 134, 268, 536, and 1072.</p>
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<h2>Important Glossaries for the Square Root of 1072</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, which is √16 = 4. </li>
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<li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers. </li>
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<li><strong>Radical form:</strong>A number expressed with a radical sign (√) is in radical form. For example, √1072 is in radical form. </li>
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<li><strong>Exponential form:</strong>A number expressed with an exponent is in exponential form. For example, 1072^(1/2) is the exponential form of the square root of 1072. </li>
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<li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 49 is a perfect square because it is 7^2.</li>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>▶</p>
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<h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>