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2026-01-01
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2026-02-28
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<p>256 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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 13500.</p>
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<h2>What is the Square Root of 13500?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 13500 is not a<a>perfect square</a>. The square root of 13500 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √13500, whereas (13500)(1/2) in exponential form. √13500 ≈ 116.1895, 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 13500</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 ideal 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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<ol><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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</ol><h2>Square Root of 13500 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 13500 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 13500 Breaking it down, we get 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5: 22 x 33 x 53</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 13500. The second step is to make pairs of those prime factors. Since 13500 is not a perfect square, the digits of the number can’t be grouped in perfect pairs.</p>
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<p>Therefore, calculating the exact<a>square root</a>of 13500 using prime factorization alone is not possible.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 13500 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 square root 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 square root using the long division method, step by step.</p>
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<p><strong>Step 1:</strong>To begin, we need to group the numbers from right to left. In the case of 13500, we need to group it as 500 and 13.</p>
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<p><strong>Step 1:</strong>To begin, we need to group the numbers from right to left. In the case of 13500, we need to group it as 500 and 13.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 13. We can say n is ‘3’ because 3 x 3 = 9, which is<a>less than</a>or equal to 13. Now the<a>quotient</a>is 3, and after subtracting 9 from 13, 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 ≤ 13. We can say n is ‘3’ because 3 x 3 = 9, which is<a>less than</a>or equal to 13. Now the<a>quotient</a>is 3, and after subtracting 9 from 13, the<a>remainder</a>is 4.</p>
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<p><strong>Step 3:</strong>Now let us bring down 500, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3 to get 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 500, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3 to get 6, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we have 6n 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<a>sum</a>of the dividend and quotient. Now we have 6n 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 6n x n ≤ 450. Let us consider n as 7, now 67 x 7 = 469.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n x n ≤ 450. Let us consider n as 7, now 67 x 7 = 469.</p>
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<p><strong>Step 6:</strong>Subtract 450 from 469, and the difference is 19, with a quotient of 37.</p>
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<p><strong>Step 6:</strong>Subtract 450 from 469, and the difference is 19, with a quotient of 37.</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 1900.</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 1900.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 746 because 746 x 2 = 1492.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 746 because 746 x 2 = 1492.</p>
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<p><strong>Step 9:</strong>Subtracting 1492 from 1900, we get the result 408.</p>
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<p><strong>Step 9:</strong>Subtracting 1492 from 1900, we get the result 408.</p>
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<p><strong>Step 10:</strong>Now the quotient is 116.2.</p>
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<p><strong>Step 10:</strong>Now the quotient is 116.2.</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 is 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 is no decimal values continue till the remainder is zero.</p>
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<p>So the square root of √13500 is approximately 116.19.</p>
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<p>So the square root of √13500 is approximately 116.19.</p>
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<h2>Square Root of 13500 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 13500 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √13500. The smallest perfect square below 13500 is 12996, and the largest perfect square above 13500 is 14400. √13500 falls somewhere between 114 and 120.</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 (13500 - 12996) ÷ (14400 - 12996) ≈ 0.1895 Using the formula, we identified the<a>decimal</a>point of our square root.</p>
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<p>The next step is adding the value we got initially to the decimal number, which is 116 + 0.1895 ≈ 116.19, so the square root of 13500 is approximately 116.19.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 13500</h2>
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<p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. 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 √135?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is 135 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 √135.</p>
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<p>Area of the square = side2 = √135 x √135 = 135.</p>
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<p>Therefore, the area of the square box is 135 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 13500 square feet is built; if each of the sides is √13500, 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>6750 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 13500 by 2, we get 6750.</p>
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<p>So half of the building measures 6750 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 √13500 x 5.</p>
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<p>Okay, lets begin</p>
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<p>580.9475</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 13500, which is approximately 116.19.</p>
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<p>The second step is to multiply 116.19 by 5.</p>
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<p>So 116.19 x 5 ≈ 580.9475.</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 (135 + 15)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is 12.</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 (135 + 15). 135 + 15 = 150, and then √150 ≈ 12.247, which is approximately 12.</p>
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<p>Therefore, the square root of (135 + 15) is approximately ±12.</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 √135 units and the width ‘w’ is 35 units.</p>
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<p>Okay, lets begin</p>
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<p>We find the perimeter of the rectangle as 99.48 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 × (√135 + 35) ≈ 2 × (11.62 + 35) ≈ 2 × 46.62 ≈ 93.24 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 13500</h2>
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<h3>1.What is √13500 in its simplest form?</h3>
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<p>The prime factorization of 13500 is 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5, so the simplest form of √13500 = √(22 x 33 x 53).</p>
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<h3>2.Mention the factors of 13500.</h3>
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<p>Factors of 13500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 675, 900, 1350, 2700, 6750, and 13500.</p>
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<h3>3.Calculate the square of 13500.</h3>
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<p>We get the square of 13500 by multiplying the number by itself, that is 13500 x 13500 = 182,250,000.</p>
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<h3>4.Is 13500 a prime number?</h3>
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<p>13500 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.13500 is divisible by?</h3>
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<p>13500 has many factors; those include 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 675, 900, 1350, 2700, 6750, and 13500.</p>
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<h2>Important Glossaries for the Square Root of 13500</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 the positive square root that has more prominence due to its uses in the real world. That is why it is also known as the principal square root.</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. For example, 16 is a perfect square because it is 42.</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>