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2026-01-01
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2026-02-28
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<p>276 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 1009</p>
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<h2>What is the Square Root of 1009?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 1009 is not a<a>perfect square</a>. The square root of 1009 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1009, whereas (1009)^(1/2) in the exponential form. √1009 ≈ 31.76476, 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 1009</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 1009 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. However, 1009 is a<a>prime number</a>and cannot be broken down into smaller prime factors. Therefore, calculating 1009 using prime factorization is not applicable.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 1009 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 1009, we need to group it as 09 and 10.</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 1009, we need to group it as 09 and 10.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 10. We can approximate n as ‘3’ because 3^2 = 9 is lesser than or equal to 10. Now the<a>quotient</a>is 3 after subtracting 10 - 9 the<a>remainder</a>is 1.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 10. We can approximate n as ‘3’ because 3^2 = 9 is lesser than or equal to 10. Now the<a>quotient</a>is 3 after subtracting 10 - 9 the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Now let us bring down 09 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.</p>
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<p><strong>Step 3:</strong>Now let us bring down 09 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.</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 ≤ 109 let us consider n as 1, now 61 x 1 = 61.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n × n ≤ 109 let us consider n as 1, now 61 x 1 = 61.</p>
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<p><strong>Step 6:</strong>Subtract 109 from 61; the difference is 48, and the quotient is 31.</p>
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<p><strong>Step 6:</strong>Subtract 109 from 61; the difference is 48, and the quotient is 31.</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 4800.</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 4800.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 637 because 637 × 7 = 4459.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 637 because 637 × 7 = 4459.</p>
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<p><strong>Step 9:</strong>Subtracting 4459 from 4800 we get the result 341.</p>
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<p><strong>Step 9:</strong>Subtracting 4459 from 4800 we get the result 341.</p>
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<p><strong>Step 10:</strong>Now the quotient is 31.7.</p>
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<p><strong>Step 10:</strong>Now the quotient is 31.7.</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 √1009 is approximately 31.76.</p>
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<p>So the square root of √1009 is approximately 31.76.</p>
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<h2>Square Root of 1009 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 1009 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √1009. The smallest perfect square<a>less than</a>1009 is 961 (31^2) and the largest perfect square<a>greater than</a>1009 is 1024 (32^2). √1009 falls somewhere between 31 and 32.</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 (1009 - 961) ÷ (1024 - 961) = 48 ÷ 63 ≈ 0.76. 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 31 + 0.76 = 31.76.</p>
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<p>So the square root of 1009 is approximately 31.76.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1009</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 √1009?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 1009 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 √1009.</p>
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<p>Area of the square = side^2</p>
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<p>= √1009 × √1009</p>
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<p>= 1009.</p>
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<p>Therefore, the area of the square box is approximately 1009 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 1009 square feet is built; if each of the sides is √1009, 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>504.5 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 1009 by 2 = 504.5</p>
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<p>So half of the building measures 504.5 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 √1009 × 5.</p>
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<p>Okay, lets begin</p>
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<p>158.8238</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 1009 which is approximately 31.76476, the second step is to multiply 31.76476 with 5.</p>
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<p>So 31.76476 × 5 ≈ 158.8238</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 (1009 + 15)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 32.0312</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 (1009 + 15) 1009 + 15 = 1024, and then √1024 = 32.</p>
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<p>Therefore, the square root of (1009 + 15) is ±32.</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 √1009 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 139.53 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 × (√1009 + 38)</p>
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<p>≈ 2 × (31.76476 + 38)</p>
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<p>= 2 × 69.76476</p>
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<p>≈ 139.53 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 1009</h2>
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<h3>1.What is √1009 in its simplest form?</h3>
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<p>Since 1009 is a prime number, the simplest form of √1009 is simply √1009.</p>
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<h3>2.Is 1009 a prime number?</h3>
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<p>Yes, 1009 is a prime number as it has no divisors other than 1 and itself.</p>
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<h3>3.What is the square of 1009?</h3>
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<p>We get the square of 1009 by multiplying the number by itself, that is 1009 × 1009 = 1,018,081.</p>
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<h3>4.Is 1009 a perfect square?</h3>
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<p>No, 1009 is not a perfect square because its square root is not an integer.</p>
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<h3>5.What is the decimal approximation of √1009?</h3>
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<p>The decimal approximation of √1009 is approximately 31.76476.</p>
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<h2>Important Glossaries for the Square Root of 1009</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 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 number:</strong>A prime number is a number greater than 1 that has no divisors other than 1 and itself. </li>
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<li><strong>Decimal approximation:</strong>A decimal approximation is a method of finding a close decimal value of a non-integer result, often used for irrational numbers.</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>