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2026-01-01
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2026-02-28
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<p>177 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 1504.</p>
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<h2>What is the Square Root of 1504?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 1504 is not a<a>perfect square</a>. The square root of 1504 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1504, whereas (1504)^(1/2) in the exponential form. √1504 ≈ 38.77886, 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 1504</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<a>long 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 1504 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 1504 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1504. Breaking it down, we get 2 × 2 × 2 × 2 × 2 × 47:<a>2^5</a>× 47.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 1504. The second step is to make pairs of those prime factors. Since 1504 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>
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<p>Therefore, calculating 1504 using prime factorization to find an exact<a>square root</a>is impossible.</p>
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<h3>Explore Our Programs</h3>
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<h2>Square Root of 1504 by Long Division Method</h2>
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<p>The long<a>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 square root using the long division method, step by step.</p>
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<p>The long<a>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 square root 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 1504, we need to group it as 04 and 15.</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 1504, we need to group it as 04 and 15.</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 15. We can say n is '3' because 3 × 3 = 9 is less than 15. Now the<a>quotient</a>is 3, and after subtracting 9 from 15, the<a>remainder</a>is 6.</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 15. We can say n is '3' because 3 × 3 = 9 is less than 15. Now the<a>quotient</a>is 3, and after subtracting 9 from 15, the<a>remainder</a>is 6.</p>
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<p><strong>Step 3:</strong>Bring down 04 to make it 604 as 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>Bring down 04 to make it 604 as 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>Find a digit x such that 6x × x is less than or equal to 604. Let’s choose x as 9, now 69 × 9 = 621, which is too large, so we try x as 8, giving us 68 × 8 = 544.</p>
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<p><strong>Step 4:</strong>Find a digit x such that 6x × x is less than or equal to 604. Let’s choose x as 9, now 69 × 9 = 621, which is too large, so we try x as 8, giving us 68 × 8 = 544.</p>
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<p><strong>Step 5:</strong>Subtract 544 from 604, the difference is 60, and the quotient is 38.</p>
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<p><strong>Step 5:</strong>Subtract 544 from 604, the difference is 60, and the quotient is 38.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 6000.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 6000.</p>
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<p><strong>Step 7:</strong>Find the new divisor which is 769 because 769 × 7 = 5383.</p>
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<p><strong>Step 7:</strong>Find the new divisor which is 769 because 769 × 7 = 5383.</p>
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<p><strong>Step 8:</strong>Subtract 5383 from 6000, we get the result 617.</p>
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<p><strong>Step 8:</strong>Subtract 5383 from 6000, we get the result 617.</p>
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<p><strong>Step 9:</strong>Now the quotient is 38.7.</p>
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<p><strong>Step 9:</strong>Now the quotient is 38.7.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get the desired decimal places.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get the desired decimal places.</p>
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<p>So, the square root of √1504 ≈ 38.77886.</p>
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<p>So, the square root of √1504 ≈ 38.77886.</p>
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<h2>Square Root of 1504 by Approximation Method</h2>
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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 1504 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect squares around 1504.</p>
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<p>The smallest perfect square less than 1504 is 1444 (38^2) and the largest perfect square<a>greater than</a>1504 is 1521 (39^2). √1504 falls between 38 and 39.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square).</p>
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<p>Using the formula (1504 - 1444) ÷ (1521 - 1444) = 60 ÷ 77 ≈ 0.779. Therefore, 38 + 0.779 = 38.779, so the square root of 1504 is approximately 38.779.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1504</h2>
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<p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of these mistakes 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 √1504?</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 1504 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 √1504.</p>
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<p>Area of the square = side^2 = √1504 × √1504 = 1504.</p>
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<p>Therefore, the area of the square box is approximately 1504 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 1504 square feet is built; if each of the sides is √1504, 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>752 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 1504 by 2 = we get 752.</p>
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<p>So half of the building measures 752 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 √1504 × 5.</p>
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<p>Okay, lets begin</p>
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<p>Approximately 193.894.</p>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 1504 which is approximately 38.779.</p>
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<p>The second step is to multiply 38.779 by 5.</p>
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<p>So, 38.779 × 5 ≈ 193.894.</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 (1400 + 104)?</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 38.77886.</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 (1400 + 104). 1400 + 104 = 1504, and then √1504 ≈ 38.77886.</p>
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<p>Therefore, the square root of (1400 + 104) is approximately ±38.77886.</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 √1504 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 153.556 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 × (√1504 + 38) ≈ 2 × (38.779 + 38) ≈ 2 × 76.779 ≈ 153.556 units.</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of 1504</h2>
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<h3>1.What is √1504 in its simplest form?</h3>
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<p>The prime factorization of 1504 is 2^5 × 47, so the simplest form of √1504 is √(2^5 × 47).</p>
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<h3>2.Mention the factors of 1504.</h3>
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<p>Factors of 1504 are 1, 2, 4, 8, 16, 32, 47, 94, 188, 376, 752, and 1504.</p>
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<h3>3.Calculate the square of 1504.</h3>
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<p>We get the square of 1504 by multiplying the number by itself: 1504 × 1504 = 2,261,016.</p>
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<h3>4.Is 1504 a prime number?</h3>
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<p>1504 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1504 is divisible by?</h3>
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<p>1504 has many factors; those are 1, 2, 4, 8, 16, 32, 47, 94, 188, 376, 752, and 1504.</p>
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<h2>Important Glossaries for the Square Root of 1504</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. For 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, 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 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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</ul><ul><li><strong>Prime factorization:</strong>Prime factorization is the process of expressing a number as the product of its prime factors.</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>