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2026-01-01
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2026-02-28
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<p>254 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 740.</p>
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<h2>What is the Square Root of 740?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 740 is not a<a>perfect square</a>. The square root of 740 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √740, whereas (740)^(1/2) in the exponential form. √740 ≈ 27.1928, 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 740</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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<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 740 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 740 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 740</p>
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<p>Breaking it down, we get 2 x 2 x 5 x 37: 2^2 x 5 x 37</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 740. The second step is to make pairs of those prime factors. Since 740 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 740 using prime factorization is impossible.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 740 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 740, we need to group it as 40 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 740, we need to group it as 40 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 is ‘2’ because 2 x 2 = 4 is less than 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 is ‘2’ because 2 x 2 = 4 is less than 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 40, 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 40, 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. We need to find the value of n such that 4n x n ≤ 340. Let us consider n as 8; now 48 x 8 = 384, which is too high. Trying n as 7, we get 47 x 7 = 329, which fits.</p>
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<p><strong>Step 4:</strong>The new divisor will be 4n. We need to find the value of n such that 4n x n ≤ 340. Let us consider n as 8; now 48 x 8 = 384, which is too high. Trying n as 7, we get 47 x 7 = 329, which fits.</p>
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<p><strong>Step 5:</strong>Subtract 329 from 340, the difference is 11, and the quotient is 27.</p>
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<p><strong>Step 5:</strong>Subtract 329 from 340, the difference is 11, 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 1100.</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 1100.</p>
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<p><strong>Step 7:</strong>The new divisor becomes 547. We determine that n is 2 because 547 x 2 = 1094.</p>
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<p><strong>Step 7:</strong>The new divisor becomes 547. We determine that n is 2 because 547 x 2 = 1094.</p>
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<p><strong>Step 8:</strong>Subtracting 1094 from 1100, we get the result 6.</p>
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<p><strong>Step 8:</strong>Subtracting 1094 from 1100, we get the result 6.</p>
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<p><strong>Step 9:</strong>Now the quotient is 27.2</p>
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<p><strong>Step 9:</strong>Now the quotient is 27.2</p>
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<p><strong>Step 10:</strong>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 10:</strong>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 √740 is approximately 27.1928.</p>
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<p>So the square root of √740 is approximately 27.1928.</p>
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<h2>Square Root of 740 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 740 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares to √740. The smallest perfect square less than 740 is 729, and the largest perfect square<a>greater than</a>740 is 784. √740 falls somewhere between 27 and 28.</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 this, (740 - 729) ÷ (784 - 729) = 11 ÷ 55 ≈ 0.2 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 27 + 0.2 = 27.2, so the square root of 740 is approximately 27.2</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 740</h2>
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<p>Students do make mistakes while finding the square root, likewise 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 √740?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 547.2 square units.</p>
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<h3>Explanation</h3>
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<p>The area of the square = side^2.</p>
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<p>The side length is given as √740.</p>
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<p>Area of the square = side^2 = √740 x √740 ≈ 27.2 x 27.2 = 739.84</p>
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<p>Therefore, the area of the square box is approximately 739.84 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 740 square feet is built; if each of the sides is √740, 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>370 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 740 by 2 = we get 370.</p>
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<p>So half of the building measures 370 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 √740 x 5.</p>
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<p>Okay, lets begin</p>
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<p>135.96</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 740, which is approximately 27.1928, the second step is to multiply 27.1928 with 5. So 27.1928 x 5 ≈ 135.964</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 (740 + 9)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 28.</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 (740 + 9). 740 + 9 = 749, and then √749 ≈ 27.37.</p>
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<p>Therefore, the square root of (740 + 9) is approximately 27.37.</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 √740 units and the width ‘w’ is 25 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 104.39 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 × (√740 + 25) ≈ 2 × (27.1928 + 25) ≈ 2 × 52.1928 ≈ 104.3856 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 740</h2>
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<h3>1.What is √740 in its simplest form?</h3>
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<p>The prime factorization of 740 is 2 x 2 x 5 x 37, so the simplest form of √740 = √(2 x 2 x 5 x 37).</p>
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<h3>2.Mention the factors of 740.</h3>
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<p>Factors of 740 are 1, 2, 4, 5, 10, 20, 37, 74, 148, 185, 370, and 740.</p>
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<h3>3.Calculate the square of 740.</h3>
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<p>We get the square of 740 by multiplying the number by itself, that is 740 x 740 = 547,600.</p>
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<h3>4.Is 740 a prime number?</h3>
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<h3>5.740 is divisible by?</h3>
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<p>740 has several factors; those are 1, 2, 4, 5, 10, 20, 37, 74, 148, 185, 370, and 740.</p>
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<h2>Important Glossaries for the Square Root of 740</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4^2 = 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 perfect square is a number that is the square of an integer. Example: 36 is a perfect square because it is 6^2.</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. Example: 7.86, 8.65, and 9.42 are decimals.</li>
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</ul><ul><li><strong>Prime factorization:</strong>Prime factorization is expressing a number as the product of its prime factors. Example: The prime factorization of 28 is 2 x 2 x 7. ```</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>