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2026-01-01
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2026-02-28
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<p>244 Learners</p>
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<p>Last updated on<strong>September 30, 2025</strong></p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 564.</p>
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<h2>What is the Square Root of 564?</h2>
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<p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 564 is not a<a>perfect square</a>. The square root of 564 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √564, whereas (564)(1/2) in exponential form. √564 ≈ 23.7487, 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 564</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>
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<ol><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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</ol><h2>Square Root of 564 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 564 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 564. Breaking it down, we get 2 x 2 x 3 x 47: 22 x 3 x 47.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 564. The second step is to make pairs of those prime factors. Since 564 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
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<p>Therefore, calculating 564 using prime factorization is not straightforward.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 564 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 564, we need to group it as 64 and 5.</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 564, we need to group it as 64 and 5.</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 5. We can say n is ‘2’ because 2 x 2 = 4 is lesser than or equal to 5. Now the<a>quotient</a>is 2, and after subtracting 4 from 5, 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 5. We can say n is ‘2’ because 2 x 2 = 4 is lesser than or equal to 5. Now the<a>quotient</a>is 2, and after subtracting 4 from 5, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Now let us bring down 64, making the new<a>dividend</a>164. Add the old<a>divisor</a>with the same number, 2 + 2, we get 4, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 64, making the new<a>dividend</a>164. Add the old<a>divisor</a>with the same number, 2 + 2, we get 4, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 4n. We need to find n such that 4n x n ≤ 164. Let us consider n as 3, now 43 x 3 = 129.</p>
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<p><strong>Step 4:</strong>The new divisor will be 4n. We need to find n such that 4n x n ≤ 164. Let us consider n as 3, now 43 x 3 = 129.</p>
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<p><strong>Step 5:</strong>Subtract 129 from 164, the difference is 35, and the quotient is 23.</p>
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<p><strong>Step 5:</strong>Subtract 129 from 164, the difference is 35, and the quotient is 23.</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 3500.</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 3500.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which is 474 because 474 x 7 = 3318.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which is 474 because 474 x 7 = 3318.</p>
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<p><strong>Step 8:</strong>Subtracting 3318 from 3500, we get the result 182.</p>
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<p><strong>Step 8:</strong>Subtracting 3318 from 3500, we get the result 182.</p>
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<p><strong>Step 9:</strong>Now the quotient is 23.7 Step 10: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.</p>
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<p><strong>Step 9:</strong>Now the quotient is 23.7 Step 10: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.</p>
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<p>So the square root of √564 is approximately 23.75.</p>
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<p>So the square root of √564 is approximately 23.75.</p>
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<h2>Square Root of 564 by Approximation Method</h2>
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<p>The approximation method is another method for finding 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 564 using the approximation method</p>
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<p>.<strong>Step 1:</strong>Now we have to find the closest perfect squares of √564. The closest perfect square less than 564 is 529 (232) and more than 564 is 576 (242). √564 falls somewhere between 23 and 24.</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) Going by the formula (564 - 529) / (576 - 529) = 35/47 ≈ 0.7447</p>
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<p>Using the formula, we identified the<a>decimal</a>point of our square root.</p>
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<p>The next step is adding the value we got initially to the decimal number which is 23 + 0.7447 ≈ 23.7447, so the square root of 564 is approximately 23.7447.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 564</h2>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make 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 √564?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square box is approximately 564 square units.</p>
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<h3>Explanation</h3>
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<p>The area of a square = side2.</p>
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<p>The side length is given as √564</p>
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<p>Area = (√564)2 = 564.</p>
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<p>Therefore, the area of the square box is approximately 564 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 564 square feet is built; if each of the sides is √564, 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>282 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 564 by 2 gives us 282.</p>
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<p>So, half of the building measures 282 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 √564 x 5.</p>
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<p>Okay, lets begin</p>
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<p>Approximately 118.74</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 564, which is approximately 23.7487.</p>
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<p>The second step is to multiply 23.7487 by 5.</p>
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<p>So, 23.7487 x 5 ≈ 118.74.</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 (544 + 20)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 24.</p>
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<h3>Explanation</h3>
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<p>To find the square root,</p>
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<p>we need to find the sum of (544 + 20). 544 + 20 = 564, and then √564 ≈ 23.7487.</p>
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<p>Therefore, the square root of (544 + 20) is approximately ±23.7487.</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 a rectangle if its length ‘l’ is √564 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 123.50 units.</p>
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<h3>Explanation</h3>
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<p>Perimeter of a rectangle = 2 × (length + width).</p>
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<p>Perimeter = 2 × (√564 + 38)</p>
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<p>= 2 × (23.7487 + 38)</p>
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<p>= 2 × 61.7487</p>
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<p>= 123.50 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 564</h2>
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<h3>1.What is √564 in its simplest form?</h3>
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<p>The prime factorization of 564 is 2 x 2 x 3 x 47. The simplest form of √564 = √(2^2 x 3 x 47)</p>
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<h3>2.Mention the factors of 564.</h3>
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<p>Factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, and 564.</p>
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<h3>3.Calculate the square of 564.</h3>
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<p>We get the square of 564 by multiplying the number by itself, that is 564 x 564 = 318,096.</p>
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<h3>4.Is 564 a prime number?</h3>
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<h3>5.564 is divisible by?</h3>
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<p>564 has many factors, including 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, and 564.</p>
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<h2>Important Glossaries for the Square Root of 564</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, 42 = 16 and the inverse of the square is the square root, that is √16 = 4.</li>
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</ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be expressed in the form of p/q, where q is not equal to zero and p and q are integers.</li>
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</ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that is more prominent due to its uses in the real world. That is the reason it is also known as the principal square root.</li>
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</ul><ul><li><strong>Approximation:</strong>A method of estimating the value of a mathematical expression when an exact answer is not needed or is difficult to obtain.</li>
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</ul><ul><li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.</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>