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2026-01-01
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2026-02-28
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<p>268 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 1245.</p>
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<h2>What is the Square Root of 1245?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 1245 is not a<a>perfect square</a>. The square root of 1245 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1245, whereas (1245)^(1/2) in the exponential form. √1245 ≈ 35.268, 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 1245</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<a>long 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 1245 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 1245 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1245 Breaking it down, we get 3 x 5 x 83: 3^1 x 5^1 x 83^1</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1245. The second step is to make pairs of those prime factors. Since 1245 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 1245 using prime factorization is impossible.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 1245 by Long Division Method</h2>
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<p>The long<a>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 long<a>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 1245, we need to group it as 45 and 12.</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 1245, we need to group it as 45 and 12.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 12. We can say n as ‘3’ because 3 x 3 is lesser than or equal to 12. Now the<a>quotient</a>is 3, and after subtracting 9 from 12, 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 12. We can say n as ‘3’ because 3 x 3 is lesser than or equal to 12. Now the<a>quotient</a>is 3, and after subtracting 9 from 12, the<a>remainder</a>is 3.</p>
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<p><strong>Step 3:</strong>Now let us bring down 45 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 3 + 3, and we get 6 which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 45 which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number, 3 + 3, and we get 6 which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 62n. We need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be 62n. We need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 62n x n ≤ 345. Let us consider n as 5. Now 625 x 5 = 3125.</p>
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<p><strong>Step 5:</strong>The next step is finding 62n x n ≤ 345. Let us consider n as 5. Now 625 x 5 = 3125.</p>
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<p><strong>Step 6:</strong>Subtract 3125 from 3450. The difference is 325, and the quotient is 35.</p>
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<p><strong>Step 6:</strong>Subtract 3125 from 3450. The difference is 325, and the quotient is 35.</p>
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<p><strong>Step 7:</strong>Since the dividend is<a>less than</a>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 32500.</p>
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<p><strong>Step 7:</strong>Since the dividend is<a>less than</a>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 32500.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 705 because 705 x 5 = 3525.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 705 because 705 x 5 = 3525.</p>
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<p><strong>Step 9:</strong>Subtracting 3525 from 32500 we get the result 29275.</p>
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<p><strong>Step 9:</strong>Subtracting 3525 from 32500 we get the result 29275.</p>
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<p><strong>Step 10:</strong>Now the quotient is 35.26</p>
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<p><strong>Step 10:</strong>Now the quotient is 35.26</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 √1245 is approximately 35.268.</p>
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<p>So the square root of √1245 is approximately 35.268.</p>
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<h2>Square Root of 1245 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 1245 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √1245. The smallest perfect square less than 1245 is 1225, and the largest perfect square<a>greater than</a>1245 is 1296. √1245 falls somewhere between 35 and 36.</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 (1245 - 1225) ÷ (1296 - 1225) = 20 / 71 ≈ 0.282 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 35 + 0.282 ≈ 35.268, so the square root of 1245 is approximately 35.268.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1245</h2>
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<p>Students do make mistakes while finding the square root, likewise forgetting about the negative square root and 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 √1245?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 1550.17 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 √1245.</p>
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<p>Area of the square = side^2 = √1245 x √1245 = 35.268 x 35.268 ≈ 1550.17</p>
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<p>Therefore, the area of the square box is approximately 1550.17 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 1245 square feet is built; if each of the sides is √1245, 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>622.5 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 1245 by 2 = 622.5</p>
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<p>So half of the building measures 622.5 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 √1245 x 5.</p>
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<p>Okay, lets begin</p>
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<p>176.34</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 1245, which is approximately 35.268.</p>
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<p>The second step is to multiply 35.268 with 5.</p>
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<p>So, 35.268 x 5 = 176.34.</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 (1245 + 10)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 35.355.</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 (1245 + 10)</p>
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<p>1245 + 10 = 1255, and then √1255 ≈ 35.355.</p>
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<p>Therefore, the square root of (1245 + 10) is approximately ±35.355.</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 √1245 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 146.536 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 × (√1245 + 38)</p>
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<p>= 2 × (35.268 + 38)</p>
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<p>= 2 × 73.268</p>
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<p>= 146.536 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 1245</h2>
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<h3>1.What is √1245 in its simplest form?</h3>
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<p>The prime factorization of 1245 is 3 x 5 x 83, so the simplest form of √1245 = √(3 x 5 x 83).</p>
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<h3>2.Mention the factors of 1245.</h3>
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<p>Factors of 1245 are 1, 3, 5, 15, 83, 249, 415, and 1245.</p>
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<h3>3.Calculate the square of 1245.</h3>
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<p>We get the square of 1245 by multiplying the number by itself, that is 1245 x 1245 = 1,550,025.</p>
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<h3>4.Is 1245 a prime number?</h3>
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<p>1245 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1245 is divisible by?</h3>
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<p>1245 has several factors; those are 1, 3, 5, 15, 83, 249, 415, and 1245.</p>
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<h2>Important Glossaries for the Square Root of 1245</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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<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 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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<li><strong>Prime factorization:</strong>It is the expression of a number as the product of its prime factors. For example, the prime factorization of 18 is 2 x 3 x 3. </li>
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<li><strong>Approximation method:</strong>A technique used to find an estimated value of a number, often used for calculating non-perfect square roots.</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>