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

3 <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 9604.</p>

4 <h2>What is the Square Root of 9604?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 9604 is a<a>perfect square</a>. The square root of 9604 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √9604, whereas (9604)^(1/2) in the exponential form. √9604 = 98, which is a<a>rational number</a>because it can be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>

6 <h2>Finding the Square Root of 9604</h2>

7 <p>The<a>prime factorization</a>method can be used for perfect square numbers. For non-perfect square numbers, the<a>long division</a>method and approximation method are used. Let us now learn the following 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 9604 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 look at how 9604 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 9604</p>

14 <p>Breaking it down, we get 2 x 2 x 7 x 7 x 7 x 7: 2^2 x 7^4</p>

15 <p><strong>Step 2:</strong>Now we have found the prime factors of 9604. The second step is to make pairs of those prime factors. Since 9604 is a perfect square, the digits of the number can be grouped in pairs. Therefore, the<a>square root</a>of 9604 using prime factorization is 2 x 7 x 7 = 98.</p>

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18 <h2>Square Root of 9604 by Long Division Method</h2>

17 <h2>Square Root of 9604 by Long Division Method</h2>

19 <p>The long<a>division</a>method is particularly useful for finding the square root of numbers, especially when they are not perfect squares. However, let's see how it works for 9604:</p>

18 <p>The long<a>division</a>method is particularly useful for finding the square root of numbers, especially when they are not perfect squares. However, let's see how it works for 9604:</p>

20 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 9604, we group it as 96 and 04.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 9604, we group it as 96 and 04.</p>

21 <p><strong>Step 2:</strong>Now, find the largest number whose square is<a>less than</a>or equal to 96. We can say that number is 9 because 9 x 9 = 81, which is less than 96. The<a>quotient</a>is 9 and the<a>remainder</a>is 96 - 81 = 15.</p>

20 <p><strong>Step 2:</strong>Now, find the largest number whose square is<a>less than</a>or equal to 96. We can say that number is 9 because 9 x 9 = 81, which is less than 96. The<a>quotient</a>is 9 and the<a>remainder</a>is 96 - 81 = 15.</p>

22 <p><strong>Step 3:</strong>Bring down the next pair, 04, making the new<a>dividend</a>1504. Add 9 to itself to get 18 as the new<a>divisor</a>'s first part.</p>

21 <p><strong>Step 3:</strong>Bring down the next pair, 04, making the new<a>dividend</a>1504. Add 9 to itself to get 18 as the new<a>divisor</a>'s first part.</p>

23 <p><strong>Step 4:</strong>Guess the largest possible digit to fill the blank in 18_ (let's call it n) such that 18n x n is less than or equal to 1504. After calculating, n comes out to be 8.</p>

22 <p><strong>Step 4:</strong>Guess the largest possible digit to fill the blank in 18_ (let's call it n) such that 18n x n is less than or equal to 1504. After calculating, n comes out to be 8.</p>

24 <p><strong>Step 5:</strong>188 x 8 = 1504, subtracting 1504 from 1504 gives a remainder of 0.</p>

23 <p><strong>Step 5:</strong>188 x 8 = 1504, subtracting 1504 from 1504 gives a remainder of 0.</p>

25 <p>Thus, the quotient is 98, and the square root of 9604 is 98.</p>

24 <p>Thus, the quotient is 98, and the square root of 9604 is 98.</p>

26 <h2>Square Root of 9604 by Approximation Method</h2>

25 <h2>Square Root of 9604 by Approximation Method</h2>

27 <p>The approximation method can be used to estimate the square roots, but it is more suited for non-perfect squares. For perfect squares like 9604, the exact square root can be found as shown in the previous methods. However, let's see an example of<a>estimation</a>:</p>

26 <p>The approximation method can be used to estimate the square roots, but it is more suited for non-perfect squares. For perfect squares like 9604, the exact square root can be found as shown in the previous methods. However, let's see an example of<a>estimation</a>:</p>

28 <p><strong>Step 1:</strong>Identify the closest perfect squares around 9604. We know that 9801 (99^2) and 9604 (98^2) are perfect squares.</p>

27 <p><strong>Step 1:</strong>Identify the closest perfect squares around 9604. We know that 9801 (99^2) and 9604 (98^2) are perfect squares.</p>

29 <p><strong>Step 2:</strong>Since 9604 is exactly 98^2, we don't need further approximation.</p>

28 <p><strong>Step 2:</strong>Since 9604 is exactly 98^2, we don't need further approximation.</p>

30 <p>The square root of 9604 is precisely 98.</p>

29 <p>The square root of 9604 is precisely 98.</p>

31 <h2>Common Mistakes and How to Avoid Them in the Square Root of 9604</h2>

30 <h2>Common Mistakes and How to Avoid Them in the Square Root of 9604</h2>

32 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of these mistakes in detail.</p>

31 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of these mistakes in detail.</p>

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33 <h3>Problem 1</h3>

34 <p>Can you help Max find the area of a square box if its side length is given as √9604?</p>

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

36 <p>The area of the square is 9604 square units.</p>

37 <h3>Explanation</h3>

38 <p>The area of the square = side^2.</p>

39 <p>The side length is given as √9604.</p>

40 <p>Area of the square = side^2 = √9604 x √9604 = 98 x 98 = 9604.</p>

41 <p>Therefore, the area of the square box is 9604 square units.</p>

42 <p>Well explained 👍</p>

43 <h3>Problem 2</h3>

44 <p>A square-shaped building measuring 9604 square feet is built; if each of the sides is √9604, what will be the square feet of half of the building?</p>

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

46 <p>4802 square feet</p>

47 <h3>Explanation</h3>

48 <p>Divide the given area by 2 as the building is square-shaped.</p>

49 <p>Dividing 9604 by 2 = 4802.</p>

50 <p>So half of the building measures 4802 square feet.</p>

51 <p>Well explained 👍</p>

52 <h3>Problem 3</h3>

53 <p>Calculate √9604 x 5.</p>

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

55 <p>490</p>

56 <h3>Explanation</h3>

57 <p>The first step is to find the square root of 9604, which is 98.</p>

58 <p>The second step is to multiply 98 by 5.</p>

59 <p>So 98 x 5 = 490.</p>

60 <p>Well explained 👍</p>

61 <h3>Problem 4</h3>

62 <p>What will be the square root of (9600 + 4)?</p>

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

64 <p>The square root is 98.</p>

65 <h3>Explanation</h3>

66 <p>To find the square root, sum (9600 + 4) = 9604.</p>

67 <p>The square root of 9604 is 98.</p>

68 <p>Therefore, the square root of (9600 + 4) is ±98.</p>

69 <p>Well explained 👍</p>

70 <h3>Problem 5</h3>

71 <p>Find the perimeter of a rectangle if its length ‘l’ is √9604 units and the width ‘w’ is 38 units.</p>

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

73 <p>The perimeter of the rectangle is 272 units.</p>

74 <h3>Explanation</h3>

75 <p>Perimeter of the rectangle = 2 × (length + width).</p>

76 <p>Perimeter = 2 × (√9604 + 38) = 2 × (98 + 38) = 2 × 136 = 272 units.</p>

77 <p>Well explained 👍</p>

78 <h2>FAQ on Square Root of 9604</h2>

79 <h3>1.What is √9604 in its simplest form?</h3>

80 <p>The prime factorization of 9604 is 2^2 x 7^4, so the simplest form of √9604 = √(2^2 x 7^4) = 98.</p>

81 <h3>2.Mention the factors of 9604.</h3>

82 <p>The factors of 9604 include 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372, 2401, 4802, and 9604.</p>

83 <h3>3.Calculate the square of 98.</h3>

84 <p>We get the square of 98 by multiplying the number by itself, that is 98 x 98 = 9604.</p>

85 <h3>4.Is 9604 a prime number?</h3>

86 <p>9604 is not a<a>prime number</a>, as it has more than two factors.</p>

87 <h3>5.9604 is divisible by?</h3>

88 <p>9604 has several factors; it is divisible by 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372, 2401, 4802, and 9604.</p>

89 <h2>Important Glossaries for the Square Root of 9604</h2>

90 <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>

91 <li><strong>Rational number:</strong>A rational number is a number that can be written in the form of p/q, where q is not equal to zero, and p and q are integers. </li>

92 <li><strong>Principal square root:</strong>A number has both positive and negative square roots. However, the positive square root is often used in real-world applications and is known as the principal square root .</li>

93 <li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 9604 is a perfect square because it is 98^2. </li>

94 <li><strong>Factorization:</strong>The process of breaking down a number into its prime factors. For example, the factorization of 9604 is 2^2 x 7^4.</li>

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

96 <p>▶</p>

97 <h2>Jaskaran Singh Saluja</h2>

98 <h3>About the Author</h3>

99 <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>

100 <h3>Fun Fact</h3>

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