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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>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 7900.</p>
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<h2>What is the Square Root of 7900?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 7900 is not a<a>perfect square</a>. The square root of 7900 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √7900, whereas (7900)^(1/2) in exponential form. √7900 ≈ 88.888, 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 7900</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<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><h2>Square Root of 7900 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 7900 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 7900 Breaking it down, we get 2 x 2 x 5 x 5 x 79: 2² x 5² x 79¹</p>
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<p><strong>Step 2:</strong>Now we have found the prime factors of 7900. The second step is to make pairs of those prime factors. Since 7900 is not a perfect square, the digits of the number can’t be grouped in complete pairs. Therefore, calculating √7900 using prime factorization is not straightforward.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 7900 by Long Division Method</h2>
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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 7900, we need to group it as 79|00.</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 7900, we need to group it as 79|00.</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 79. We can say n is 8 because 8 x 8 = 64, which is less than 79. Now the<a>quotient</a>is 8 after subtracting 64 from 79; the<a>remainder</a>is 15.</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 79. We can say n is 8 because 8 x 8 = 64, which is less than 79. Now the<a>quotient</a>is 8 after subtracting 64 from 79; the<a>remainder</a>is 15.</p>
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<p><strong>Step 3:</strong>Now let us bring down 00, which makes the new<a>dividend</a>1500. Add the old<a>divisor</a>with the same number: 8 + 8 = 16, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 00, which makes the new<a>dividend</a>1500. Add the old<a>divisor</a>with the same number: 8 + 8 = 16, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>Now, find n such that 16n × n ≤ 1500. Let us consider n as 9; now 169 x 9 = 1521, which is larger than 1500, so we consider n as 8.</p>
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<p><strong>Step 4:</strong>Now, find n such that 16n × n ≤ 1500. Let us consider n as 9; now 169 x 9 = 1521, which is larger than 1500, so we consider n as 8.</p>
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<p><strong>Step 5:</strong>Subtract 1500 from 1456 (168 x 8 = 1456); the difference is 44, and the quotient is 88.</p>
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<p><strong>Step 5:</strong>Subtract 1500 from 1456 (168 x 8 = 1456); the difference is 44, and the quotient is 88.</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 zeros to the dividend. Now the new dividend is 4400.</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 zeros to the dividend. Now the new dividend is 4400.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which will be 176. Let’s find n such that 176n x n ≤ 4400. Suppose n is 2, then 1762 x 2 = 3524.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which will be 176. Let’s find n such that 176n x n ≤ 4400. Suppose n is 2, then 1762 x 2 = 3524.</p>
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<p><strong>Step 8:</strong>Subtract 3524 from 4400, we get 876.</p>
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<p><strong>Step 8:</strong>Subtract 3524 from 4400, we get 876.</p>
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<p><strong>Step 9:</strong>Now the quotient is 88.8</p>
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<p><strong>Step 9:</strong>Now the quotient is 88.8</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. So the square root of √7900 ≈ 88.88</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. So the square root of √7900 ≈ 88.88</p>
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<h2>Square Root of 7900 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 7900 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √7900. The smallest perfect square less than 7900 is 7744 (88^2) and the largest perfect square<a>greater than</a>7900 is 7921 (89^2). √7900 falls somewhere between 88 and 89.</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: (7900 - 7744) ÷ (7921 - 7744) = 156 / 177 ≈ 0.881 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: 88 + 0.881 ≈ 88.881, so the square root of 7900 is approximately 88.881.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 7900</h2>
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<p>Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's explore some common mistakes in more 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 √7900?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is 7900 square units.</p>
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<h3>Explanation</h3>
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<p>The area of the square = side². The side length is given as √7900. Area of the square = side² = √7900 x √7900 = 7900. Therefore, the area of the square box is 7900 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 plot measuring 7900 square meters is built; if each of the sides is √7900, what will be the square meters of half of the plot?</p>
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<p>Okay, lets begin</p>
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<p>3950 square meters.</p>
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<h3>Explanation</h3>
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<p>We can just divide the given area by 2 as the plot is square-shaped. Dividing 7900 by 2 = 3950. So half of the plot measures 3950 square meters.</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<p>Calculate √7900 x 5.</p>
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<p>Okay, lets begin</p>
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<p>Approximately 444.44.</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 7900, which is approximately 88.88. The second step is to multiply 88.88 by 5. So 88.88 x 5 ≈ 444.44.</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 (7900 + 21)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is 89.</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 (7900 + 21). 7900 + 21 = 7921, and then √7921 = 89. Therefore, the square root of (7900 + 21) is ±89.</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 √7900 units and the width ‘w’ is 40 units.</p>
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<p>Okay, lets begin</p>
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<p>The perimeter of the rectangle is approximately 257.76 units.</p>
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<h3>Explanation</h3>
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<p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√7900 + 40) = 2 × (88.88 + 40) = 2 × 128.88 ≈ 257.76 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 7900</h2>
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<h3>1.What is √7900 in its simplest form?</h3>
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<p>The prime factorization of 7900 is 2² × 5² × 79, so the simplest radical form of √7900 is √(2² × 5² × 79).</p>
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<h3>2.Mention the factors of 7900.</h3>
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<p>Factors of 7900 include 1, 2, 4, 5, 10, 20, 25, 50, 79, 158, 395, 790, 1580, 1975, 3950, and 7900.</p>
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<h3>3.Calculate the square of 7900.</h3>
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<p>The square of 7900 is obtained by multiplying the number by itself: 7900 × 7900 = 62410000.</p>
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<h3>4.Is 7900 a prime number?</h3>
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<p>7900 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.7900 is divisible by?</h3>
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<p>7900 is divisible by 1, 2, 4, 5, 10, 20, 25, 50, 79, 158, 395, 790, 1580, 1975, 3950, and 7900.</p>
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<h2>Important Glossaries for the Square Root of 7900</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, 5² = 25 and the inverse of the square is the square root, so √25 = 5. </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>Principal square root:</strong>A number has both positive and negative square roots; the principal square root is the positive one, which is most often used in real-world applications. </li>
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<li><strong>Prime factorization:</strong>Breaking down a number into the product of its prime factors. For example, the prime factorization of 90 is 2 × 3² × 5. </li>
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<li><strong>Decimal:</strong>A decimal is a number that includes a whole number and a fractional part separated by a decimal point, such as 3.14 or 88.88.</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>