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2026-01-01
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2026-02-28
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<p>200 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 fields of vehicle design, finance, etc. Here, we will discuss the square root of 1184.</p>
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<h2>What is the Square Root of 1184?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 1184 is not a<a>perfect square</a>. The square root of 1184 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1184, whereas (1184)^(1/2) in the<a>exponential form</a>. √1184 ≈ 34.4093, 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 1184</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 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 1184 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 1184 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1184 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 37:<a>2^5</a>x 37</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1184. The second step is to make pairs of those prime factors. Since 1184 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 1184 using prime factorization gives an approximate value.</p>
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<h3>Explore Our Programs</h3>
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<h3>Square Root of 1184 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 1184, we need to group it as 84 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 1184, we need to group it as 84 and 11.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is close to 11. We can say n is '3' because 3 x 3 = 9 which is lesser than or equal to 11. Now the<a>quotient</a>is 3 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 close to 11. We can say n is '3' because 3 x 3 = 9 which is lesser than or equal to 11. Now the<a>quotient</a>is 3 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 84 which is the new<a>dividend</a>. 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 84 which is the new<a>dividend</a>. 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>The new divisor will be 60 (6n), and we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be 60 (6n), and we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 60n × n ≤ 284; let us consider n as 4, now 60 x 4 = 240.</p>
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<p><strong>Step 5:</strong>The next step is finding 60n × n ≤ 284; let us consider n as 4, now 60 x 4 = 240.</p>
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<p><strong>Step 6:</strong>Subtract 284 from 240, the difference is 44.</p>
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<p><strong>Step 6:</strong>Subtract 284 from 240, the difference is 44.</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 4400.</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 4400.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 698 because 698 x 6 = 4188.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 698 because 698 x 6 = 4188.</p>
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<p><strong>Step 9:</strong>Subtracting 4188 from 4400, we get the result 212.</p>
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<p><strong>Step 9:</strong>Subtracting 4188 from 4400, we get the result 212.</p>
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<p><strong>Step 10:</strong>Now the quotient is 34.4.</p>
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<p><strong>Step 10:</strong>Now the quotient is 34.4.</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 √1184 is approximately 34.409.</p>
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<p>So the square root of √1184 is approximately 34.409.</p>
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<h3>Square Root of 1184 by Approximation Method</h3>
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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 1184 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares to √1184. The smallest perfect square less than 1184 is 1156 (34^2), and the largest perfect square<a>greater than</a>1184 is 1296 (36^2). √1184 falls somewhere between 34 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). Using the formula (1184 - 1156) ÷ (1296 - 1156) = 28 / 140 ≈ 0.2. 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 34 + 0.2 = 34.2.</p>
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<p>So the square root of 1184 is approximately 34.409.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1184</h2>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping the long division method, 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 √1184?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 1400.377 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 √1184.</p>
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<p>Area of the square = side^2 = √1184 x √1184 = 34.4093 × 34.4093 ≈ 1400.377.</p>
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<p>Therefore, the area of the square box is approximately 1400.377 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 1184 square feet is built; if each of the sides is √1184, 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>592 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 1184 by 2 = we get 592.</p>
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<p>So half of the building measures 592 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 √1184 x 5.</p>
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<p>Okay, lets begin</p>
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<p>Approximately 172.0465</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 1184 which is approximately 34.4093, the second step is to multiply 34.4093 with 5.</p>
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<p>So 34.4093 x 5 ≈ 172.0465.</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 (1184 + 16)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 35.3553</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 (1184 + 16). 1184 + 16 = 1200, and then √1200 ≈ 34.6410.</p>
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<p>Therefore, the square root of (1184 + 16) is approximately ±34.6410.</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 √1184 units and the width ‘w’ is 40 units.</p>
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<p>Okay, lets begin</p>
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<p>The perimeter of the rectangle is approximately 148.8186 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 × (√1184 + 40) ≈ 2 × (34.4093 + 40) ≈ 2 × 74.4093 ≈ 148.8186 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 1184</h2>
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<h3>1.What is √1184 in its simplest form?</h3>
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<p>The prime factorization of 1184 is 2 x 2 x 2 x 2 x 2 x 37, so the simplest form of √1184 = √(2^5 x 37) = 4√(74).</p>
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<h3>2.Mention the factors of 1184.</h3>
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<p>Factors of 1184 are 1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592, and 1184.</p>
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<h3>3.Calculate the square of 1184.</h3>
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<p>We get the square of 1184 by multiplying the number by itself, that is 1184 x 1184 = 1,401,536.</p>
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<h3>4.Is 1184 a prime number?</h3>
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<p>1184 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1184 is divisible by?</h3>
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<p>1184 has many factors; those are 1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592, and 1184.</p>
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<h2>Important Glossaries for the Square Root of 1184</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, where q is not equal to zero and p and q are integers.<strong></strong></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 the principal square root.</li>
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</ul><ul><li><strong>Prime factorization:</strong>Prime factorization is the process of expressing a number as a product of its prime factors.</li>
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</ul><ul><li><strong>Long division method:</strong>The long division method is a technique used to find the square root of non-perfect squares by using systematic division and subtraction steps.</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>