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2026-01-01
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2026-02-28
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<p>250 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 the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields like engineering, finance, etc. Here, we will discuss the square root of 824.</p>
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<h2>What is the Square Root of 824?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 824 is not a<a>perfect square</a>. The square root of 824 is expressed in both radical and<a>exponential form</a>.</p>
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<p>In radical form, it is expressed as √824, whereas in exponential form, it is expressed as (824)(1/2). √824 ≈ 28.7228, 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 824</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<a>long 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><h3>Square Root of 824 by Prime Factorization Method</h3>
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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 824 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 824 Breaking it down, we get 2 x 2 x 2 x 103: 23 x 1031</p>
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<p><strong>Step 2:</strong>Now we have found the prime factors of 824. The next step is to make pairs of those prime factors. Since 824 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
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<p>Therefore, calculating √824 using prime factorization is impractical for exact results.</p>
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<h3>Explore Our Programs</h3>
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<h3>Square Root of 824 by Long Division Method</h3>
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<p>The long<a>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 long<a>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 824, we need to group it as 24 and 8.</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 824, we need to group it as 24 and 8.</p>
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<p><strong>Step 2:</strong>Now, we need to find a number whose square is<a>less than</a>or equal to 8. We can say n as '2' because 2 x 2 = 4, which is less than 8. Now the<a>quotient</a>is 2, and after subtracting 4 from 8, the<a>remainder</a>is 4.</p>
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<p><strong>Step 2:</strong>Now, we need to find a number whose square is<a>less than</a>or equal to 8. We can say n as '2' because 2 x 2 = 4, which is less than 8. Now the<a>quotient</a>is 2, and after subtracting 4 from 8, the<a>remainder</a>is 4.</p>
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<p><strong>Step 3:</strong>Bring down 24, making the new<a>dividend</a>424. Add the old<a>divisor</a>with the quotient, 2 + 2, to get 4, which will be part of our new divisor.</p>
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<p><strong>Step 3:</strong>Bring down 24, making the new<a>dividend</a>424. Add the old<a>divisor</a>with the quotient, 2 + 2, to get 4, which will be part of our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor is 42n. We need to find the value of n such that 42n x n ≤ 424. Let's consider n as 9, then 42 x 9 = 378.</p>
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<p><strong>Step 4:</strong>The new divisor is 42n. We need to find the value of n such that 42n x n ≤ 424. Let's consider n as 9, then 42 x 9 = 378.</p>
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<p><strong>Step 5:</strong>Subtract 378 from 424, the difference is 46, and the quotient is 29.</p>
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<p><strong>Step 5:</strong>Subtract 378 from 424, the difference is 46, and the quotient is 29.</p>
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<p><strong>Step 6:</strong>Since there is a remainder, add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4600.</p>
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<p><strong>Step 6:</strong>Since there is a remainder, add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4600.</p>
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<p><strong>Step 7:</strong>Find a new divisor that is 586 because 586 x 8 = 4688.</p>
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<p><strong>Step 7:</strong>Find a new divisor that is 586 because 586 x 8 = 4688.</p>
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<p><strong>Step 8:</strong>Subtracting 4688 from 4600 gives the result -88.</p>
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<p><strong>Step 8:</strong>Subtracting 4688 from 4600 gives the result -88.</p>
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<p><strong>Step 9:</strong>Continue these steps until we get two numbers after the decimal point or until the remainder is zero. So the square root of √824 is approximately 28.72.</p>
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<p><strong>Step 9:</strong>Continue these steps until we get two numbers after the decimal point or until the remainder is zero. So the square root of √824 is approximately 28.72.</p>
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<h3>Square Root of 824 by Approximation Method</h3>
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<p>The approximation method is another method for finding square roots, and it is an easy method for estimating the square root of a given number. Now let us learn how to find the square root of 824 using the approximation method.</p>
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<p><strong>Step 1:</strong>Find the closest perfect squares of √824. The smallest perfect square less than 824 is 784 (282), and the largest perfect square<a>greater than</a>824 is 841 (292). √824 falls between 28 and 29.</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>
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<p>Using the formula, (824 - 784) / (841 - 784) = 40 / 57 ≈ 0.70 Adding this to the smaller perfect square's root gives us 28 + 0.70 = 28.70, so the square root of 824 is approximately 28.72.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 824</h2>
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<p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few common 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 √824?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 824 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 √824.</p>
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<p>Area of the square = side² = √824 x √824 = 824.</p>
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<p>Therefore, the area of the square box is approximately 824 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 measures 824 square feet. If each of the sides is √824, 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>412 square feet</p>
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<h3>Explanation</h3>
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<p>To find half of the area of the square-shaped building, divide 824 by 2.</p>
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<p>Dividing 824 by 2 gives 412.</p>
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<p>Therefore, half of the building measures 412 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 √824 x 5.</p>
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<p>Okay, lets begin</p>
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<p>Approximately 143.61</p>
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<h3>Explanation</h3>
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<p>First, find the square root of 824, which is approximately 28.72.</p>
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<p>The second step is to multiply 28.72 by 5.</p>
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<p>So, 28.72 x 5 ≈ 143.61.</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 (824 + 16)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 28.5.</p>
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<h3>Explanation</h3>
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<p>To find the square root, first calculate the sum of (824 + 16). 824 + 16 = 840, and the square root of 840 is approximately 28.5.</p>
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<p>Therefore, the square root of (824 + 16) is approximately ±28.5.</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 √824 units and the width 'w' is 20 units.</p>
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<p>Okay, lets begin</p>
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<p>The perimeter of the rectangle is approximately 97.44 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 × (√824 + 20) = 2 × (28.72 + 20) = 2 × 48.72 = 97.44 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 824</h2>
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<h3>1.What is √824 in its simplest form?</h3>
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<p>The prime factorization of 824 is 2 x 2 x 2 x 103, so the simplest form of √824 = √(23 x 103).</p>
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<h3>2.Mention the factors of 824.</h3>
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<p>Factors of 824 are 1, 2, 4, 8, 103, 206, 412, and 824.</p>
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<h3>3.Calculate the square of 824.</h3>
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<p>The square of 824 is found by multiplying the number by itself: 824 x 824 = 678,976.</p>
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<h3>4.Is 824 a prime number?</h3>
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<h3>5.824 is divisible by?</h3>
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<p>824 has several factors; it is divisible by 1, 2, 4, 8, 103, 206, 412, and 824.</p>
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<h2>Important Glossaries for the Square Root of 824</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. Example: 4² = 16 and the inverse is the square root, √16 = 4. </li>
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<li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction. Its decimal goes on forever without repeating. </li>
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<li><strong>Perfect square:</strong>A perfect square is an integer that is the square of an integer. For example, 1, 4, 9, 16, etc. </li>
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<li><strong>Prime factorization:</strong>Breaking down a number into its basic building blocks, which are prime numbers. </li>
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<li><strong>Approximation:</strong>Estimating a number's value close to its true value, often used when precise values are hard to find.</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>