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2026-01-01
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2026-02-28
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<p>251 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 154.</p>
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<h2>What is the Square Root of 154?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 154 is not a<a>perfect square</a>. The square root of 154 is expressed in both radical and<a>exponential form</a>. In the radical form it is expressed as √154, whereas in exponential form it is (154)^(1/2). √154 ≈ 12.40967, 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 154</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 154 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 154 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 154 Breaking it down, we get 2 x 7 x 11: 2^1 x 7^1 x 11^1</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 154. The second step is to make pairs of those prime factors. Since 154 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 154 using prime factorization is not straightforward.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 154 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 154, we group it as 54 and 1.</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 154, we group it as 54 and 1.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 1. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 1. Now the<a>quotient</a>is 1; after subtracting 1 - 1, the<a>remainder</a>is 0.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is 1. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 1. Now the<a>quotient</a>is 1; after subtracting 1 - 1, the<a>remainder</a>is 0.</p>
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<p><strong>Step 3:</strong>Now let us bring down 54, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1, we get 2, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 54, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 1 + 1, we get 2, 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 2n 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 2n 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 2n x n ≤ 54. Let's consider n as 2; now 2 x 2 x 2 = 44.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n x n ≤ 54. Let's consider n as 2; now 2 x 2 x 2 = 44.</p>
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<p><strong>Step 6:</strong>Subtract 54 from 44, the difference is 10, and the quotient is 12.</p>
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<p><strong>Step 6:</strong>Subtract 54 from 44, the difference is 10, and the quotient is 12.</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 zeros to the dividend. Now the new dividend is 1000.</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 zeros to the dividend. Now the new dividend is 1000.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 249 because 249 x 4 = 996.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 249 because 249 x 4 = 996.</p>
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<p><strong>Step 9:</strong>Subtracting 996 from 1000 we get the result 4.</p>
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<p><strong>Step 9:</strong>Subtracting 996 from 1000 we get the result 4.</p>
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<p><strong>Step 10:</strong>Now the quotient is 12.4</p>
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<p><strong>Step 10:</strong>Now the quotient is 12.4</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 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 √154 ≈ 12.41</p>
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<p>So the square root of √154 ≈ 12.41</p>
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<h2>Square Root of 154 by Approximation Method</h2>
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<p>The approximation method is another method for finding square roots, and it is an easy way to find the square root of a given number. Now let us learn how to find the square root of 154 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square of √154. The smallest perfect square<a>less than</a>154 is 144, and the largest perfect square<a>greater than</a>154 is 169. √154 falls somewhere between 12 and 13.</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 (154 - 144) ÷ (169 - 144) = 0.4 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: 12 + 0.4 = 12.4.</p>
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<p>So the square root of 154 is approximately 12.4.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 154</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 √154?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 154 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 √154.</p>
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<p>Area of the square = side²</p>
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<p>= √154 x √154</p>
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<p>= 154.</p>
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<p>Therefore, the area of the square box is approximately 154 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 154 square feet is built; if each of the sides is √154, 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>77 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 154 by 2 = we get 77.</p>
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<p>So half of the building measures 77 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 √154 x 5.</p>
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<p>Okay, lets begin</p>
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<p>Approximately 62.05</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 154, which is approximately 12.41.</p>
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<p>The second step is to multiply 12.41 with 5.</p>
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<p>So 12.41 x 5 ≈ 62.05.</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 (144 + 10)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 12.65.</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 (144 + 10).</p>
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<p>144 + 10 = 154, and then √154 ≈ 12.41.</p>
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<p>Therefore, the square root of (144 + 10) is approximately ±12.41.</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 √154 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 100.82 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 × (√154 + 38)</p>
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<p>= 2 × (12.41 + 38)</p>
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<p>≈ 2 × 50.41</p>
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<p>= 100.82 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 154</h2>
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<h3>1.What is √154 in its simplest form?</h3>
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<p>The prime factorization of 154 is 2 x 7 x 11, so the simplest form of √154 = √(2 x 7 x 11).</p>
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<h3>2.Mention the factors of 154.</h3>
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<p>Factors of 154 are 1, 2, 7, 11, 14, 22, 77, and 154.</p>
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<h3>3.Calculate the square of 154.</h3>
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<p>We get the square of 154 by multiplying the number by itself, that is 154 x 154 = 23716.</p>
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<h3>4.Is 154 a prime number?</h3>
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<h3>5.154 is divisible by?</h3>
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<p>154 has several factors; those are 1, 2, 7, 11, 14, 22, 77, and 154.</p>
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<h2>Important Glossaries for the Square Root of 154</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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<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>Perfect square:</strong>A number that is the square of an integer. For example, 144 is a perfect square because it is 12². </li>
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<li><strong>Approximation:</strong>The process of finding values that are close to the exact value. </li>
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<li><strong>Prime factorization:</strong>Breaking down a number into its basic prime number components. For example, the prime factorization of 154 is 2 x 7 x 11.</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>