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2026-01-01
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2026-02-28
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<p>282 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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 800.</p>
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<h2>What is the Square Root of 800?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 800 is not a<a>perfect square</a>. The square root of 800 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √800, whereas in the exponential form it is (800)^(1/2). √800 ≈ 28.28427, 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 800</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 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 800 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 800 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 800 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 5 x 5:<a>2^5</a>x 5^2</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 800. The second step is to make pairs of those prime factors. Since 800 is not a perfect square, the digits of the number can’t be grouped into complete pairs.</p>
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<p>Therefore, calculating 800 using prime factorization involves taking out pairs and simplifying under the radical.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 800 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 800, we need to group it as 00 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 800, we need to group it as 00 and 8.</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 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 n 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>Now let us bring down 00, which is the new<a>dividend</a>, making it 400. 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 00, which is the new<a>dividend</a>, making it 400. 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, where n is a digit that when multiplied by 4n gives us a number less than or equal to 400. Let’s consider n as 7, now 47 x 7 = 329.</p>
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<p><strong>Step 4:</strong>The new divisor will be 4n, where n is a digit that when multiplied by 4n gives us a number less than or equal to 400. Let’s consider n as 7, now 47 x 7 = 329.</p>
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<p><strong>Step 5:</strong>Subtract 329 from 400, the difference is 71, and the quotient is 27.</p>
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<p><strong>Step 5:</strong>Subtract 329 from 400, the difference is 71, and the quotient is 27.</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 7100.</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 7100.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor that is 5 because 545 x 5 = 2725.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor that is 5 because 545 x 5 = 2725.</p>
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<p><strong>Step 8:</strong>Subtracting 2725 from 7100, we get the result 4375.</p>
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<p><strong>Step 8:</strong>Subtracting 2725 from 7100, we get the result 4375.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.</p>
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<p>So the square root of √800 is approximately 28.28.</p>
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<p>So the square root of √800 is approximately 28.28.</p>
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<h2>Square Root of 800 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 800 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √800.</p>
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<p>The smallest perfect square less than 800 is 784, and the largest perfect square<a>greater than</a>800 is 841. √800 falls somewhere between 28 and 29.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (800 - 784) ÷ (841 - 784) ≈ 0.28.</p>
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<p>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 28 + 0.28 ≈ 28.28, so the square root of 800 is approximately 28.28.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 800</h2>
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<p>Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. 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 √800?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is 800 square units.</p>
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<h3>Explanation</h3>
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<p>The area of the square = side².</p>
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<p>The side length is given as √800.</p>
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<p>Area of the square = side² = √800 × √800 = 800</p>
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<p>Therefore, the area of the square box is 800 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 800 square feet is built. If each of the sides is √800, 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>400 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 800 by 2, we get 400.</p>
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<p>So half of the building measures 400 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 √800 × 5.</p>
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<p>Okay, lets begin</p>
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<p>141.42</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 800, which is approximately 28.28.</p>
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<p>The second step is to multiply 28.28 with 5.</p>
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<p>So 28.28 × 5 ≈ 141.42.</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 (800 + 1)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 28.31.</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 (800 + 1). 800 + 1 = 801, and then √801 ≈ 28.31.</p>
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<p>Therefore, the square root of (800 + 1) is approximately ±28.31.</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 √800 units and the width ‘w’ is 38 units.</p>
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<p>Okay, lets begin</p>
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<p>We find the perimeter of the rectangle as approximately 132.57 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 × (√800 + 38) = 2 × (28.28 + 38) = 2 × 66.28 ≈ 132.57 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 800</h2>
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<h3>1.What is √800 in its simplest form?</h3>
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<p>The prime factorization of 800 is 2 x 2 x 2 x 2 x 2 x 5 x 5, so the simplest form of √800 = √(2^5 x 5^2) = 20√2.</p>
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<h3>2.Mention the factors of 800.</h3>
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<p>Factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, and 800.</p>
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<h3>3.Calculate the square of 800.</h3>
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<p>We get the square of 800 by multiplying the number by itself, that is 800 x 800 = 640,000.</p>
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<h3>4.Is 800 a prime number?</h3>
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<h3>5.800 is divisible by?</h3>
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<p>800 has many factors; those are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, and 800.</p>
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<h2>Important Glossaries for the Square Root of 800</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. 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 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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</ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. For example, 16 is a perfect square because it is 4².</li>
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</ul><ul><li><strong>Long division method:</strong>A method used to find the square root of non-perfect square numbers by dividing and finding the quotient iteratively.</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>