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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>If a number is multiplied by itself, the result is a square. The inverse operation is called finding the square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 7488.</p>

4 <h2>What is the Square Root of 7488?</h2>

5 <p>The<a>square</a>root is the inverse of squaring a<a>number</a>. 7488 is not a<a>perfect square</a>. The square root of 7488 can be expressed in both radical and exponential forms. In radical form, it is expressed as √7488, whereas in<a>exponential form</a>it is (7488)^(1/2). √7488 ≈ 86.521, which is an<a>irrational number</a>because it cannot be expressed as a<a>ratio</a>of two<a>integers</a>.</p>

6 <h2>Finding the Square Root of 7488</h2>

7 <p>For perfect square numbers, the<a>prime factorization</a>method is used. However, for non-perfect square numbers like 7488, the<a>long division</a>method and approximation method are used. Let us now learn these methods:</p>

8 <ul><li>Prime factorization method</li>

9 <li>Long division method</li>

10 <li>Approximation method</li>

11 </ul><h2>Square Root of 7488 by Prime Factorization Method</h2>

12 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us see how 7488 is broken down into its prime factors:</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 7488: Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 3 x 13 x 12.</p>

14 <p><strong>Step 2:</strong>Now that we have found the prime factors of 7488, the next step is to make pairs of those prime factors. Since 7488 is not a perfect square, the digits of the number cannot be grouped in pairs. Therefore, calculating the<a>square root</a>of 7488 using prime factorization directly is not straightforward.</p>

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17 <h2>Square Root of 7488 by Long Division Method</h2>

16 <h2>Square Root of 7488 by Long Division Method</h2>

18 <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>

17 <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>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 7488, we need to group it as 88 and 74.</p>

18 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 7488, we need to group it as 88 and 74.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 74. We can choose n as ‘8’ because 8 x 8 = 64 is less than 74. Now the<a>quotient</a>is 8, and after subtracting 64 from 74, the<a>remainder</a>is 10.</p>

19 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 74. We can choose n as ‘8’ because 8 x 8 = 64 is less than 74. Now the<a>quotient</a>is 8, and after subtracting 64 from 74, the<a>remainder</a>is 10.</p>

21 <p><strong>Step 3:</strong>Bring down 88, making the new<a>dividend</a>1088. Add the old<a>divisor</a>8 to itself to get 16, which will be part of our new divisor.</p>

20 <p><strong>Step 3:</strong>Bring down 88, making the new<a>dividend</a>1088. Add the old<a>divisor</a>8 to itself to get 16, which will be part of our new divisor.</p>

22 <p><strong>Step 4:</strong>The new divisor will be 16n. We need to find n such that 16n x n is less than or equal to 1088. Choosing n as 6, we find 16 x 6 x 6 = 576.</p>

21 <p><strong>Step 4:</strong>The new divisor will be 16n. We need to find n such that 16n x n is less than or equal to 1088. Choosing n as 6, we find 16 x 6 x 6 = 576.</p>

23 <p><strong>Step 5:</strong>Subtract 576 from 1088 to get 512, and the quotient becomes 86.</p>

22 <p><strong>Step 5:</strong>Subtract 576 from 1088 to get 512, and the quotient becomes 86.</p>

24 <p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point, allowing us to bring down two zeros. The new dividend becomes 51200.</p>

23 <p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a<a>decimal</a>point, allowing us to bring down two zeros. The new dividend becomes 51200.</p>

25 <p><strong>Step 7:</strong>Now we find a new divisor, 172, such that 172n x n is less than or equal to 51200. Choosing n as 2, we find 172 x 2 x 2 = 688.</p>

24 <p><strong>Step 7:</strong>Now we find a new divisor, 172, such that 172n x n is less than or equal to 51200. Choosing n as 2, we find 172 x 2 x 2 = 688.</p>

26 <p><strong>Step 8:</strong>Subtract 688 from 51200 to get 50512, and continue this process until the desired accuracy is achieved. So the square root of √7488 is approximately 86.52.</p>

25 <p><strong>Step 8:</strong>Subtract 688 from 51200 to get 50512, and continue this process until the desired accuracy is achieved. So the square root of √7488 is approximately 86.52.</p>

27 <h2>Square Root of 7488 by Approximation Method</h2>

26 <h2>Square Root of 7488 by Approximation Method</h2>

28 <p>The approximation method is another way to find square roots and is an easy method for estimating the square root of a given number. Let us learn how to find the square root of 7488 using the approximation method.</p>

27 <p>The approximation method is another way to find square roots and is an easy method for estimating the square root of a given number. Let us learn how to find the square root of 7488 using the approximation method.</p>

29 <p><strong>Step 1:</strong>First, find the closest perfect squares to 7488. The closest perfect squares are 7225 (85^2) and 7569 (87^2). √7488 falls between 85 and 87.</p>

28 <p><strong>Step 1:</strong>First, find the closest perfect squares to 7488. The closest perfect squares are 7225 (85^2) and 7569 (87^2). √7488 falls between 85 and 87.</p>

30 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). Using the formula (7488 - 7225) / (7569 - 7225) = 263 / 344 = 0.7645.</p>

29 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). Using the formula (7488 - 7225) / (7569 - 7225) = 263 / 344 = 0.7645.</p>

31 <p><strong>Step 3:</strong>Adding this to the smaller perfect square root gives 85 + 0.7645 ≈ 85.76. So, the approximate square root of 7488 using this method is about 85.76.</p>

30 <p><strong>Step 3:</strong>Adding this to the smaller perfect square root gives 85 + 0.7645 ≈ 85.76. So, the approximate square root of 7488 using this method is about 85.76.</p>

32 <h2>Common Mistakes and How to Avoid Them in the Square Root of 7488</h2>

31 <h2>Common Mistakes and How to Avoid Them in the Square Root of 7488</h2>

33 <p>Students often make mistakes when finding square roots, such as forgetting the negative square root or skipping steps in methods like long division. Let's look at some common mistakes in detail.</p>

32 <p>Students often make mistakes when finding square roots, such as forgetting the negative square root or skipping steps in methods like long division. Let's look at some common mistakes in detail.</p>

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34 <h3>Problem 1</h3>

35 <p>Can you help Max find the area of a square box if its side length is given as √7488?</p>

36 <p>Okay, lets begin</p>

37 <p>The area of the square is approximately 7488 square units.</p>

38 <h3>Explanation</h3>

39 <p>The area of a square = side^2. The side length is given as √7488. Area of the square = (√7488)^2 = 7488. Therefore, the area of the square box is approximately 7488 square units.</p>

40 <p>Well explained 👍</p>

41 <h3>Problem 2</h3>

42 <p>A square-shaped building measuring 7488 square feet is built. If each of the sides is √7488, what will be the square feet of half of the building?</p>

43 <p>Okay, lets begin</p>

44 <p>3744 square feet.</p>

45 <h3>Explanation</h3>

46 <p>We can divide the given area by 2 since the building is square-shaped. Dividing 7488 by 2 gives 3744. So, half of the building measures 3744 square feet.</p>

47 <p>Well explained 👍</p>

48 <h3>Problem 3</h3>

49 <p>Calculate √7488 x 5.</p>

50 <p>Okay, lets begin</p>

51 <p>432.605</p>

52 <h3>Explanation</h3>

53 <p>The first step is to find the square root of 7488, which is approximately 86.521. The second step is to multiply this by 5. 86.521 x 5 = 432.605.</p>

54 <p>Well explained 👍</p>

55 <h3>Problem 4</h3>

56 <p>What will be the square root of (7488 + 12)?</p>

57 <p>Okay, lets begin</p>

58 <p>The square root is approximately 87.</p>

59 <h3>Explanation</h3>

60 <p>To find the square root, we need to find the sum of (7488 + 12). 7488 + 12 = 7500. Then, √7500 ≈ 86.603. Therefore, the square root of (7488 + 12) is approximately ±86.603.</p>

61 <p>Well explained 👍</p>

62 <h3>Problem 5</h3>

63 <p>Find the perimeter of the rectangle if its length ‘l’ is √7488 units and the width ‘w’ is 38 units.</p>

64 <p>Okay, lets begin</p>

65 <p>The perimeter of the rectangle is approximately 249.042 units.</p>

66 <h3>Explanation</h3>

67 <p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√7488 + 38). Perimeter = 2 × (86.521 + 38) = 2 × 124.521 = 249.042 units.</p>

68 <p>Well explained 👍</p>

69 <h2>FAQ on Square Root of 7488</h2>

70 <h3>1.What is √7488 in its simplest form?</h3>

71 <p>The prime factorization of 7488 is 2 x 2 x 2 x 2 x 3 x 3 x 13 x 12. Thus, the simplest form of √7488 is expressed in<a>terms</a>of its prime factors.</p>

72 <h3>2.Mention the factors of 7488.</h3>

73 <p>Factors of 7488 include 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 52, 78, 104, 156, 312, 488, 624, 936, 1872, 3744, and 7488.</p>

74 <h3>3.Calculate the square of 86.</h3>

75 <p>We get the square of 86 by multiplying the number by itself: 86 x 86 = 7396.</p>

76 <h3>4.Is 7488 a prime number?</h3>

77 <p>7488 is not a<a>prime number</a>, as it has more than two factors.</p>

78 <h3>5.7488 is divisible by?</h3>

79 <p>7488 has many factors, including 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 52, 78, 104, 156, 312, 488, 624, 936, 1872, 3744, and 7488.</p>

80 <h2>Important Glossaries for the Square Root of 7488</h2>

81 <ul><li><strong>Square root:</strong>The square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the inverse is the square root: √16 = 4. </li>

82 <li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction, meaning it cannot be written as p/q where p and q are integers and q ≠ 0. </li>

83 <li><strong>Principal square root:</strong>A number has both positive and negative square roots, but the positive square root is commonly used in practical applications and is known as the principal square root. </li>

84 <li><strong>Prime factorization:</strong>Breaking down a number into the product of its prime factors. For example, 7488 can be expressed as 2 x 2 x 2 x 2 x 3 x 3 x 13 x 12. </li>

85 <li><strong>Long division method:</strong>A method used to find the square root of a number, particularly useful for non-perfect squares, involving several systematic steps.</li>

86 </ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>

87 <p>▶</p>

88 <h2>Jaskaran Singh Saluja</h2>

89 <h3>About the Author</h3>

90 <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>

91 <h3>Fun Fact</h3>

92 <p>: He loves to play the quiz with kids through algebra to make kids love it.</p>