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2026-01-01
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2026-02-28
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<p>217 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 1134.</p>
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<h2>What is the Square Root of 1134?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 1134 is not a<a>perfect square</a>. The square root of 1134 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1134, whereas (1134)^(1/2) in the exponential form. √1134 ≈ 33.661, 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 1134</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 1134 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 1134 is broken down into its prime factors:</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1134 Breaking it down, we get 2 x 3 x 3 x 3 x 3 x 7: (2^1 times<a>3^4</a>times 7^1)</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1134. The second step is to make pairs of those prime factors. Since 1134 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 1134 using prime factorization is impossible.</p>
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<h3>Square Root of 1134 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 1134, we need to group it as 34 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 1134, we need to group it as 34 and 11.</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 11. We can say n as ‘3’ because 3 × 3 = 9 is lesser than or equal to 11. Now the<a>quotient</a>is 3, and after subtracting 11 - 9, the<a>remainder</a>is 2.</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 11. We can say n as ‘3’ because 3 × 3 = 9 is lesser than or equal to 11. Now the<a>quotient</a>is 3, and after subtracting 11 - 9, the<a>remainder</a>is 2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 34, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3 = 6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 34, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 3 + 3 = 6, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum 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 sum 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 ≤ 234. Let's consider n as 3, now 63 × 3 = 189.</p>
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<p><strong>Step 5:</strong>The next step is finding 6n × n ≤ 234. Let's consider n as 3, now 63 × 3 = 189.</p>
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<p><strong>Step 6:</strong>Subtract 234 from 189; the difference is 45, and the quotient is 33.</p>
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<p><strong>Step 6:</strong>Subtract 234 from 189; the difference is 45, and the quotient is 33.</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 4500.</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 4500.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 336, because 336 × 9 = 3024.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 336, because 336 × 9 = 3024.</p>
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<p><strong>Step 9:</strong>Subtracting 3024 from 4500 gives us the result 1476.</p>
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<p><strong>Step 9:</strong>Subtracting 3024 from 4500 gives us the result 1476.</p>
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<p><strong>Step 10:</strong>Now the quotient is 33.6.</p>
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<p><strong>Step 10:</strong>Now the quotient is 33.6.</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. So the square root of √1134 is approximately 33.66.</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. So the square root of √1134 is approximately 33.66.</p>
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<h3>Square Root of 1134 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 1134 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √1134. The smallest perfect square of 1134 is 1024, and the largest perfect square of 1134 is 1156. √1134 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>that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (1134 - 1024) / (1156 - 1024) ≈ 0.91. 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 + 0.91 = 32.91, so the square root of 1134 is approximately 33.66.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1134</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 √1134?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 1283.676 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 √1134.</p>
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<p>Area of the square = side² = √1134 × √1134 ≈ 33.66 × 33.66 ≈ 1134.</p>
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<p>Therefore, the area of the square box is approximately 1134 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 1134 square feet is built; if each of the sides is √1134, 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>567 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 1134 by 2 = we get 567.</p>
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<p>So half of the building measures 567 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 √1134 × 5.</p>
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<p>Okay, lets begin</p>
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<p>168.305</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 1134, which is approximately 33.661.</p>
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<p>The second step is to multiply 33.661 with 5.</p>
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<p>So 33.661 × 5 ≈ 168.305.</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 (1034 + 100)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is 34.</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 (1034 + 100). 1034 + 100 = 1134, and then √1134 ≈ 33.66.</p>
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<p>Therefore, the square root of (1034 + 100) is ±33.66.</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 √1134 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 143.32 units.</p>
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<h3>Explanation</h3>
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<p>Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√1134 + 38) ≈ 2 × (33.66 + 38) ≈ 2 × 71.66 ≈ 143.32 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 1134</h2>
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<h3>1.What is √1134 in its simplest form?</h3>
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<p>The prime factorization of 1134 is 2 × 3 × 3 × 3 × 3 × 7, so the simplest form of √1134 = √(2 × 3 × 3 × 3 × 3 × 7).</p>
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<h3>2.Mention the factors of 1134.</h3>
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<p>Factors of 1134 are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 81, 111, 222, 333, 567, and 1134.</p>
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<h3>3.Calculate the square of 1134.</h3>
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<p>We get the square of 1134 by multiplying the number by itself, that is 1134 × 1134 = 1,286,756.</p>
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<h3>4.Is 1134 a prime number?</h3>
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<p>1134 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1134 is divisible by?</h3>
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<p>1134 has many factors; those are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 81, 111, 222, 333, 567, and 1134.</p>
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<h2>Important Glossaries for the Square Root of 1134</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 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>Prime factorization is breaking down a number into its basic prime number factors. For example, the prime factorization of 18 is 2 × 3 × 3.</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>