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2026-01-01
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2026-02-28
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<p>206 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 798.</p>
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<h2>What is the Square Root of 798?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 798 is not a<a>perfect square</a>. The square root of 798 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √798, whereas (798)^(1/2) in the exponential form. √798 ≈ 28.2512, 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 798</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 798 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 798 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 798 Breaking it down, we get 2 x 3 x 7 x 19: 2¹ x 3¹ x 7¹ x 19¹</p>
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<p><strong>Step 2:</strong>Now that we found the prime factors of 798, the second step is to make pairs of those prime factors. Since 798 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.</p>
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<p>Therefore, calculating 798 using prime factorization is impossible.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 798 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 798, we need to group it as 98 and 7.</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 798, we need to group it as 98 and 7.</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 7. We can say n as ‘2’ because 2² = 4 is lesser than or equal to 7. Now the<a>quotient</a>is 2, and after subtracting 4 from 7, the<a>remainder</a>is 3.</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 7. We can say n as ‘2’ because 2² = 4 is lesser than or equal to 7. Now the<a>quotient</a>is 2, and after subtracting 4 from 7, the<a>remainder</a>is 3.</p>
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<p><strong>Step 3:</strong>Now let us bring down 98, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2 to get 4, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 98, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2 to get 4, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 4n, and we need to find the value of n such that 4n × n ≤ 398.</p>
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<p><strong>Step 4:</strong>The new divisor will be 4n, and we need to find the value of n such that 4n × n ≤ 398.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 398. Let us consider n as 7, now 47 × 7 = 329.</p>
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<p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 398. Let us consider n as 7, now 47 × 7 = 329.</p>
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<p><strong>Step 6:</strong>Subtract 329 from 398; the difference is 69, and the quotient is 27.</p>
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<p><strong>Step 6:</strong>Subtract 329 from 398; the difference is 69, and the quotient is 27.</p>
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<p><strong>Step 7:</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 6900.</p>
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<p><strong>Step 7:</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 6900.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 545 because 545 × 5 = 2725.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 545 because 545 × 5 = 2725.</p>
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<p><strong>Step 9:</strong>Subtracting 2725 from 6900, we get the result 4175.</p>
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<p><strong>Step 9:</strong>Subtracting 2725 from 6900, we get the result 4175.</p>
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<p><strong>Step 10:</strong>Now the quotient is 28.2</p>
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<p><strong>Step 10:</strong>Now the quotient is 28.2</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
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<p>So the square root of √798 is approximately 28.25.</p>
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<p>So the square root of √798 is approximately 28.25.</p>
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<h2>Square Root of 798 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 798 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares to √798.</p>
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<p>The smallest perfect square less than 798 is 784, and the largest perfect square<a>greater than</a>798 is 841. √798 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>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)</p>
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<p>Using the formula (798 - 784) / (841 - 784) = 14 / 57 ≈ 0.246 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 + 0.246 = 28.246, so the square root of 798 is approximately 28.25.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 798</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 √798?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 798 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 √798.</p>
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<p>Area of the square = side² = √798 × √798 = 798.</p>
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<p>Therefore, the area of the square box is approximately 798 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 798 square feet is built; if each of the sides is √798, 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>399 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 798 by 2 gives us 399.</p>
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<p>So half of the building measures 399 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 √798 × 5.</p>
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<p>Okay, lets begin</p>
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<p>Approximately 141.256</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 798, which is approximately 28.2512.</p>
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<p>The second step is to multiply 28.2512 by 5.</p>
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<p>So, 28.2512 × 5 ≈ 141.256.</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 (798 + 2)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 28.3019</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 (798 + 2). 798 + 2 = 800, and then √800 ≈ 28.3019.</p>
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<p>Therefore, the square root of (798 + 2) is approximately ±28.3019.</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 √798 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 132.5 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 × (√798 + 38) = 2 × (28.2512 + 38) = 2 × 66.2512 ≈ 132.5 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 798</h2>
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<h3>1.What is √798 in its simplest form?</h3>
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<p>The prime factorization of 798 is 2 × 3 × 7 × 19, so the simplest form of √798 = √(2 × 3 × 7 × 19).</p>
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<h3>2.Mention the factors of 798.</h3>
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<p>Factors of 798 are 1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 57, 114, 133, 266, 399, and 798.</p>
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<h3>3.Calculate the square of 798.</h3>
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<p>We get the square of 798 by multiplying the number by itself, that is 798 × 798 = 636804.</p>
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<h3>4.Is 798 a prime number?</h3>
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<h3>5.798 is divisible by?</h3>
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<p>798 has many factors; those are 1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 57, 114, 133, 266, 399, and 798.</p>
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<h2>Important Glossaries for the Square Root of 798</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>Principal square root:</strong>A number has both positive and negative square roots; however, it is always a positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.</li>
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</ul><ul><li><strong>Prime factorization:</strong>The expression of a number as the product of its prime factors is called prime factorization. Example: The prime factorization of 18 is 2 × 3 × 3.</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>