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2026-01-01
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2026-02-28
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<p>197 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 1130.</p>
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<h2>What is the Square Root of 1130?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 1130 is not a<a>perfect square</a>. The square root of 1130 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1130, whereas in exponential form it is expressed as (1130)^(1/2). √1130 ≈ 33.6309, 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 1130</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><h3>Square Root of 1130 by Prime Factorization Method</h3>
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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 1130 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1130 Breaking it down, we get 2 x 5 x 113: 2¹ x 5¹ x 113¹</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1130. Since 1130 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 1130 using prime factorization is not straightforward.</p>
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<h3>Square Root of 1130 by Long Division Method</h3>
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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 1130, we need to group it as 30 and 11.</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 1130, we need to group it as 30 and 11.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 11. We can say n as ‘3’ because 3 x 3 = 9, which is<a>less than</a>or equal to 11. Now the<a>quotient</a>is 3, subtracting 9 from 11 gives the<a>remainder</a>2.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 11. We can say n as ‘3’ because 3 x 3 = 9, which is<a>less than</a>or equal to 11. Now the<a>quotient</a>is 3, subtracting 9 from 11 gives the<a>remainder</a>2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 30, making the new<a>dividend</a>230. 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 30, making the new<a>dividend</a>230. 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>We need to find a digit n such that 6n x n is less than or equal to 230. Let n be 3, so 63 x 3 = 189.</p>
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<p><strong>Step 4:</strong>We need to find a digit n such that 6n x n is less than or equal to 230. Let n be 3, so 63 x 3 = 189.</p>
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<p><strong>Step 5:</strong>Subtract 189 from 230, the difference is 41, and the quotient is 33.</p>
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<p><strong>Step 5:</strong>Subtract 189 from 230, the difference is 41, and the quotient is 33.</p>
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<p><strong>Step 6:</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 zeros to the dividend. Now the new dividend is 4100.</p>
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<p><strong>Step 6:</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 zeros to the dividend. Now the new dividend is 4100.</p>
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<p><strong>Step 7:</strong>Find a new digit n such that 663n x n is less than or equal to 4100. Let n be 6, so 6636 x 6 = 39816.</p>
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<p><strong>Step 7:</strong>Find a new digit n such that 663n x n is less than or equal to 4100. Let n be 6, so 6636 x 6 = 39816.</p>
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<p><strong>Step 8:</strong>Subtracting 39816 from 4100 gives the result 284.</p>
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<p><strong>Step 8:</strong>Subtracting 39816 from 4100 gives the result 284.</p>
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<p><strong>Step 9:</strong>The quotient is now 33.6. Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero. So the square root of √1130 is approximately 33.63.</p>
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<p><strong>Step 9:</strong>The quotient is now 33.6. Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero. So the square root of √1130 is approximately 33.63.</p>
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<h3>Square Root of 1130 by Approximation Method</h3>
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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 1130 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares of √1130. The smallest perfect square less than 1130 is 1024 and the largest perfect square<a>greater than</a>1130 is 1156. √1130 falls somewhere between 32 and 34.</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). Using the formula: (1130 - 1024) / (1156 - 1024) = 106 / 132 ≈ 0.803. 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 32 + 0.803 = 32.803, so the square root of 1130 is approximately 33.63.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1130</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 √1130?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 1130 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 √1130.</p>
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<p>Area of the square = (√1130)² = 1130.</p>
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<p>Therefore, the area of the square box is approximately 1130 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 1130 square feet is built; if each of the sides is √1130, 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>565 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 1130 by 2 gives us 565.</p>
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<p>So half of the building measures 565 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 √1130 x 5.</p>
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<p>Okay, lets begin</p>
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<p>Approximately 168.15</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 1130, which is approximately 33.63.</p>
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<p>The second step is to multiply 33.63 by 5.</p>
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<p>So 33.63 x 5 = 168.15.</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 (1024 + 6)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 32.0624.</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 (1024 + 6) which equals 1030. √1030 ≈ 32.0624.</p>
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<p>Therefore, the square root of (1024 + 6) is approximately 32.0624.</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 √1130 units and the width ‘w’ is 20 units.</p>
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<p>Okay, lets begin</p>
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<p>The perimeter of the rectangle is approximately 107.26 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 × (√1130 + 20) = 2 × (33.63 + 20) = 2 × 53.63 = 107.26 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 1130</h2>
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<h3>1.What is √1130 in its simplest form?</h3>
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<p>The simplest form of √1130 is √(2 x 5 x 113).</p>
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<h3>2.Mention the factors of 1130.</h3>
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<p>Factors of 1130 are 1, 2, 5, 10, 113, 226, 565, and 1130.</p>
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<h3>3.Calculate the square of 1130.</h3>
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<p>We get the square of 1130 by multiplying the number by itself, that is 1130 x 1130 = 1,276,900.</p>
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<h3>4.Is 1130 a prime number?</h3>
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<p>1130 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1130 is divisible by?</h3>
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<p>1130 is divisible by 1, 2, 5, 10, 113, 226, 565, and 1130.</p>
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<h2>Important Glossaries for the Square Root of 1130</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. For 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>Prime factorization:</strong>Prime factorization involves expressing a number as the product of its prime factors. For example, the prime factorization of 1130 is 2 x 5 x 113.</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>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.<strong></strong></li>
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</ul><ul><li><strong>Long division method:</strong>A method used to find the square root of non-perfect squares by dividing the number into pairs and using iterative subtraction.</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>