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2026-01-01
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2026-02-28
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<p>274 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 7380.</p>
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<h2>What is the Square Root of 7380?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 7380 is not a<a>perfect square</a>. The square root of 7380 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √7380, whereas (7380)^(1/2) in the exponential form. √7380 ≈ 85.909, 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 7380</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>and approximation methods 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 7380 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 7380 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 7380 Breaking it down, we get 2 x 2 x 3 x 5 x 5 x 41: (2^2) x 3^1 x 5^2 x 41^1</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 7380. The second step is to make pairs of those prime factors. Since 7380 is not a perfect square, the digits of the number can’t be grouped entirely in pairs. Therefore, calculating √7380 using prime factorization directly is not feasible.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 7380 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 7380, we need to group it as 80 and 73.</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 7380, we need to group it as 80 and 73.</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 73. We can say n is ‘8’ because 8^2 = 64 is less than 73. Now the<a>quotient</a>is 8, and after subtracting 64 from 73, the<a>remainder</a>is 9.</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 73. We can say n is ‘8’ because 8^2 = 64 is less than 73. Now the<a>quotient</a>is 8, and after subtracting 64 from 73, the<a>remainder</a>is 9.</p>
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<p><strong>Step 3:</strong>Now let us bring down 80, which is the new<a>dividend</a>. 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 80, which is the new<a>dividend</a>. 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>The new divisor will be the sum of the dividend and quotient. Now we get 16n as the new divisor, we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the dividend and quotient. Now we get 16n as the new divisor, we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 16n × n ≤ 980. Let us consider n as 5, now 16 x 5 x 5 = 825</p>
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<p><strong>Step 5:</strong>The next step is finding 16n × n ≤ 980. Let us consider n as 5, now 16 x 5 x 5 = 825</p>
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<p><strong>Step 6:</strong>Subtract 980 from 825; the difference is 155, and the quotient is 85.</p>
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<p><strong>Step 6:</strong>Subtract 980 from 825; the difference is 155, and the quotient is 85.</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 15500.</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 15500.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 859 because 859 x 9 = 7731</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 859 because 859 x 9 = 7731</p>
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<p><strong>Step 9:</strong>Subtracting 7731 from 15500, we get the result 7779.</p>
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<p><strong>Step 9:</strong>Subtracting 7731 from 15500, we get the result 7779.</p>
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<p><strong>Step 10:</strong>Now the quotient is 85.9</p>
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<p><strong>Step 10:</strong>Now the quotient is 85.9</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 is no decimal values, continue till the remainder is zero. So the square root of √7380 is approximately 85.91.</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 is no decimal values, continue till the remainder is zero. So the square root of √7380 is approximately 85.91.</p>
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<h2>Square Root of 7380 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 7380 using the approximation method</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √7380. The smallest perfect square less than 7380 is 7225, and the largest perfect square<a>greater than</a>7380 is 7569. √7380 falls somewhere between 85 and 87.</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 (7380 - 7225) ÷ (7569 - 7225) = 155 ÷ 344 = 0.4506 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 85 + 0.45 = 85.45, so the square root of 7380 is approximately 85.45.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 7380</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 √7380?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 545,640.81 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 √7380. Area of the square = side² = √7380 x √7380 = 85.91 x 85.91 ≈ 7390.5481 Therefore, the area of the square box is approximately 545,640.81 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 7380 square feet is built; if each of the sides is √7380, 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>3690 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. Dividing 7380 by 2 = we get 3690 So half of the building measures 3690 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 √7380 x 5.</p>
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<p>Okay, lets begin</p>
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<p>429.55</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 7380, which is approximately 85.91. The second step is to multiply 85.91 by 5. So, 85.91 x 5 ≈ 429.55.</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 (7380 + 20)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 86.</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 (7380 + 20). 7380 + 20 = 7400, and then √7400 ≈ 86.166 Therefore, the square root of (7380 + 20) is approximately 86.</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 √7380 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 247.82 units.</p>
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<h3>Explanation</h3>
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<p>Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√7380 + 38) = 2 × (85.91 + 38) = 2 × 123.91 ≈ 247.82 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 7380</h2>
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<h3>1.What is √7380 in its simplest form?</h3>
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<p>The prime factorization of 7380 is 2 x 2 x 3 x 5 x 5 x 41, so the simplest form of √7380 = √(2² x 3 x 5² x 41).</p>
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<h3>2.Mention the factors of 7380.</h3>
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<p>Factors of 7380 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 41, 60, 82, 123, 164, 205, 246, 246, 410, 615, 738, 1230, 1845, 2460, 3690, and 7380.</p>
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<h3>3.Calculate the square of 7380.</h3>
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<p>We get the square of 7380 by multiplying the number by itself, which is 7380 x 7380 = 54,464,400.</p>
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<h3>4.Is 7380 a prime number?</h3>
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<p>7380 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.7380 is divisible by?</h3>
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<p>7380 has many factors; those are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 41, 60, 82, 123, 164, 205, 246, 246, 410, 615, 738, 1230, 1845, 2460, 3690, and 7380.</p>
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<h2>Important Glossaries for the Square Root of 7380</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, 9² = 81, and the inverse of the square is the square root, which is √81 = 9. </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; however, it is always the 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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<li><strong>Prime factorization:</strong>Prime factorization is the expression of a number as a product of its prime factors. </li>
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<li><strong>Approximation:</strong>Approximation is the process of finding a value that is close enough to the correct answer, usually within a tolerable error range.</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>