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2026-01-01
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2026-02-28
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<p>210 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 like vehicle design, finance, etc. Here, we will discuss the square root of 1452.</p>
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<h2>What is the Square Root of 1452?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 1452 is not a<a>perfect square</a>. The square root of 1452 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1452, whereas (1452)^(1/2) in the exponential form. √1452 ≈ 38.093, 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 1452</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 1452 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's look at how 1452 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1452 Breaking it down, we get 2 × 2 × 3 × 11 × 11: 2^2 × 3^1 × 11^2</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1452. The second step is to make pairs of those prime factors. Since 1452 is not a perfect square, therefore the digits of the number can’t be grouped in pairs completely.</p>
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<p>Therefore, calculating 1452 using prime factorization alone for exact<a>square root</a>is impossible.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 1452 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 with, we need to group the numbers from right to left. In the case of 1452, we need to group it as 52 and 14.</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 1452, we need to group it as 52 and 14.</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 14. We can say n is ‘3’ because 3 × 3 = 9, which is lesser than or equal to 14. Now the<a>quotient</a>is 3, and after subtracting 9 from 14, the<a>remainder</a>is 5.</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 14. We can say n is ‘3’ because 3 × 3 = 9, which is lesser than or equal to 14. Now the<a>quotient</a>is 3, and after subtracting 9 from 14, the<a>remainder</a>is 5.</p>
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<p><strong>Step 3:</strong>Now let us bring down 52 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3 we get 6 which will be our new divisor with a blank space for the next digit.</p>
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<p><strong>Step 3:</strong>Now let us bring down 52 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3 we get 6 which will be our new divisor with a blank space for the next digit.</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 get 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 get 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 × n ≤ 552. Let us consider n as 8, now 68 × 8 = 544.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n × n ≤ 552. Let us consider n as 8, now 68 × 8 = 544.</p>
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<p><strong>Step 6:</strong>Subtract 552 from 544; the difference is 8, and the quotient is 38.</p>
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<p><strong>Step 6:</strong>Subtract 552 from 544; the difference is 8, and the quotient is 38.</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 800.</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 800.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 761 because 761 × 1 = 761.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 761 because 761 × 1 = 761.</p>
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<p><strong>Step 9:</strong>Subtracting 761 from 800 we get the result 39.</p>
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<p><strong>Step 9:</strong>Subtracting 761 from 800 we get the result 39.</p>
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<p><strong>Step 10:</strong>Now the quotient is 38.1.</p>
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<p><strong>Step 10:</strong>Now the quotient is 38.1.</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 √1452 is approximately 38.09.</p>
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<p>So the square root of √1452 is approximately 38.09.</p>
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<h2>Square Root of 1452 by Approximation Method</h2>
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<p>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 1452 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square to √1452.</p>
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<p>The smallest perfect square of 1452 is 1444 and the largest perfect square of 1452 is 1521. √1452 falls somewhere between 38 and 39.</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 (1452 - 1444) / (1521 - 1444) ≈ 0.093.</p>
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<p>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 38 + 0.093 = 38.093, so the square root of 1452 is approximately 38.093.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1452</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 √1452?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 2109.864 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 √1452.</p>
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<p>Area of the square = side² = √1452 × √1452 ≈ 38.093 × 38.093 ≈ 1452.</p>
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<p>Therefore, the area of the square box is approximately 2109.864 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 1452 square feet is built; if each of the sides is √1452, 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>726 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 1452 by 2 = 726</p>
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<p>So half of the building measures 726 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 √1452 × 5.</p>
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<p>Okay, lets begin</p>
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<p>Approximately 190.465</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 1452, which is approximately 38.093.</p>
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<p>The second step is to multiply 38.093 with 5.</p>
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<p>So 38.093 × 5 ≈ 190.465.</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 (1444 + 8)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 38</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 (1444 + 8). 1444 + 8 = 1452, and then √1452 ≈ 38.</p>
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<p>Therefore, the square root of (1444 + 8) is approximately ±38.</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 √1452 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 191.186 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 × (√1452 + 38) ≈ 2 × (38.093 + 38) = 2 × 76.093 = 152.186 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 1452</h2>
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<h3>1.What is √1452 in its simplest form?</h3>
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<p>The prime factorization of 1452 is 2 × 2 × 3 × 11 × 11, so the simplest form of √1452 = √(2 × 2 × 3 × 11 × 11).</p>
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<h3>2.Mention the factors of 1452.</h3>
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<p>Factors of 1452 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 121, 132, 242, 363, 484, 726, and 1452.</p>
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<h3>3.Calculate the square of 1452.</h3>
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<p>We get the square of 1452 by multiplying the number by itself, that is 1452 × 1452 = 2,108,304.</p>
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<h3>4.Is 1452 a prime number?</h3>
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<p>1452 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1452 is divisible by?</h3>
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<p>1452 has many factors; those are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 121, 132, 242, 363, 484, 726, and 1452.</p>
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<h2>Important Glossaries for the Square Root of 1452</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, 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>Breaking down a composite number into its prime factors.</li>
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</ul><ul><li><strong>Approximation:</strong>Estimating a value close to the actual value, often used in finding square roots of non-perfect squares.</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>