Rivalry2

HTML Diff

2 added 2 removed

Original 2026-01-01

Modified 2026-02-21

1 - <p>551 Learners</p>

1 + <p>625 Learners</p>

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

3 <p>The square root of 96 is the inverse operation of squaring a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 96. It contains both positive and a negative root, where the positive root is called the principal square root.</p>

4 <h2>What Is the Square Root of 96?</h2>

5 <p>The<a>square</a>root<a>of</a>96 is ±9.79795897113. The positive value,9.79795897113 is the solution of the<a>equation</a>x2 = 96.</p>

6 <p>As defined, the square root is just the inverse of squaring a<a>number</a>, so, squaring 9.79795897113 will result in 96. The square root of 96 is expressed as √96 in radical form, where the ‘√’ sign is called “radical” sign. In<a>exponential form</a>, it is written as (96)1/2 </p>

7 <h2>Finding the Square Root of 96</h2>

8 <p>We can find the<a>square root</a>of 96 through various methods. They are:</p>

9 <p>Prime factorization method</p>

10 <p>Long<a>division</a>method</p>

11 <p>Approximation/Estimation method </p>

12 <h3>Square Root of 96 By Prime Factorization Method</h3>

13 <p>The<a>prime factorization</a>of 96 involves breaking down a number into its<a>factors</a>. Divide 96 by<a>prime numbers</a>, and continue to divide the quotients until they can’t be separated anymore. After factorizing 96, make pairs out of the factors to get the square root. If there exists numbers which cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs</p>

14 <p>So, Prime factorization of 96 = 3 × 2 ×2×2 ×2 ×2 </p>

15 <p>for 96, two pairs of factors 2 obtained, but a single 3 and a single 2 are also obtained.</p>

16 <p>So, it can be expressed as √96 = √(3×2 ×2× 2 × 2 × 2) = 4√6</p>

17 <p>4√6 is the simplest radical form of √96 </p>

18 <h3>Explore Our Programs</h3>

19 - <p>No Courses Available</p>

20 <h3>Square Root of 96 by Long Division Method</h3>

19 <h3>Square Root of 96 by Long Division Method</h3>

21 <p>This is a method used for obtaining the square root for non-<a>perfect squares</a>, mainly. It usually involves the division of the<a>dividend</a>by the<a>divisor</a>, getting a<a>quotient</a>and a<a>remainder</a>too sometimes.</p>

20 <p>This is a method used for obtaining the square root for non-<a>perfect squares</a>, mainly. It usually involves the division of the<a>dividend</a>by the<a>divisor</a>, getting a<a>quotient</a>and a<a>remainder</a>too sometimes.</p>

22 <p>Follow the steps to calculate the square root of 96:</p>

21 <p>Follow the steps to calculate the square root of 96:</p>

23 <p><strong>Step 1 :</strong>Write the number 96, and draw a bar above the pair of digits from right to left.</p>

22 <p><strong>Step 1 :</strong>Write the number 96, and draw a bar above the pair of digits from right to left.</p>

24 <p> <strong>Step 2 :</strong>Now, find the greatest number whose square is<a>less than</a>or equal to 96. Here, it is9, Because 92=81 < 96</p>

23 <p> <strong>Step 2 :</strong>Now, find the greatest number whose square is<a>less than</a>or equal to 96. Here, it is9, Because 92=81 < 96</p>

25 <p><strong>Step 3 :</strong>Now divide 96 by 9 (the number we got from Step 2) such that we get 9 as quotient, and we get a remainder. Double the divisor 9, we get 18 and then the largest possible number A1=7 is chosen such that when 7 is written beside the new divisor, 18, a 3-digit number is formed →187 and multiplying 7 with 187 gives 1309 which is less than 1500.</p>

24 <p><strong>Step 3 :</strong>Now divide 96 by 9 (the number we got from Step 2) such that we get 9 as quotient, and we get a remainder. Double the divisor 9, we get 18 and then the largest possible number A1=7 is chosen such that when 7 is written beside the new divisor, 18, a 3-digit number is formed →187 and multiplying 7 with 187 gives 1309 which is less than 1500.</p>

26 <p>Repeat the process until you reach remainder 0</p>

25 <p>Repeat the process until you reach remainder 0</p>

27 <p>We are left with the remainder, 18791 (refer to the picture), after some iterations and keeping the division till here, at this point </p>

26 <p>We are left with the remainder, 18791 (refer to the picture), after some iterations and keeping the division till here, at this point </p>

28 <p> <strong>Step 4 :</strong>The quotient obtained is the square root. In this case, it is 9.797…</p>

27 <p> <strong>Step 4 :</strong>The quotient obtained is the square root. In this case, it is 9.797…</p>

29 <h3>Square Root of 96 by Approximation Method</h3>

28 <h3>Square Root of 96 by Approximation Method</h3>

30 <p>Approximation or<a>estimation</a>of square root is not the exact square root, but it is an estimate.Here, through this method, an approximate value of square root is found by guessing.</p>

29 <p>Approximation or<a>estimation</a>of square root is not the exact square root, but it is an estimate.Here, through this method, an approximate value of square root is found by guessing.</p>

31 <p>Follow the steps below:</p>

30 <p>Follow the steps below:</p>

32 <p><strong>Step 1 :</strong>Identify the square roots of the perfect squares above and below 96</p>

31 <p><strong>Step 1 :</strong>Identify the square roots of the perfect squares above and below 96</p>

33 <p>Below : 81→ square root of 81 = 9 ……..(<a>i</a>)</p>

32 <p>Below : 81→ square root of 81 = 9 ……..(<a>i</a>)</p>

34 <p> Above : 100 →square root of 100= 10 ……..(ii)</p>

33 <p> Above : 100 →square root of 100= 10 ……..(ii)</p>

35 <p><strong>Step 2 :</strong>Divide 96 with one of 9 or 10 </p>

34 <p><strong>Step 2 :</strong>Divide 96 with one of 9 or 10 </p>

36 <p> If we choose 9, and divide 96 by 9, we get 10.666 …….(iii)</p>

35 <p> If we choose 9, and divide 96 by 9, we get 10.666 …….(iii)</p>

37 <p><strong> Step 3:</strong>Find the<a>average</a>of 9 (from (i)) and 10.666 (from (iii))</p>

36 <p><strong> Step 3:</strong>Find the<a>average</a>of 9 (from (i)) and 10.666 (from (iii))</p>

38 <p>(9+10.666)/2 = 9.8333</p>

37 <p>(9+10.666)/2 = 9.8333</p>

39 <p>Hence, 9.8333 is the approximate square root of 96 </p>

38 <p>Hence, 9.8333 is the approximate square root of 96 </p>

39 + <h2>Download Worksheets</h2>

40 <h3>Problem 1</h3>

41 <p>Simplify 5√96 + 13√96 ?</p>

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

43 <p>5√96+13√96</p>

44 <p>= √96(5+13)</p>

45 <p>= 9.797 ⤬ (5+13)</p>

46 <p>=18 ⤬ 9.797</p>

47 <p>= 176.346</p>

48 <p>Answer : 176.346 </p>

49 <h3>Explanation</h3>

50 <p>Taking out the common part √96, adding the values inside bracket. √96= 9.797, so multiplying the square root value with the sum. </p>

51 <p>Well explained 👍</p>

52 <h3>Problem 2</h3>

53 <p>Multiply √96 with √6</p>

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

55 <p> √96 ⤬ √6</p>

56 <p>= 4√6⤬ √6</p>

57 <p>=4 ⤬6</p>

58 <p>=24</p>

59 <p>Answer : 24 </p>

60 <h3>Explanation</h3>

61 <p>multiplying the simplest radical form of √96 with √6. </p>

62 <p>Well explained 👍</p>

63 <h3>Problem 3</h3>

64 <p>Compare √96 and √97</p>

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

66 <p> √96 ≅ 9.797,</p>

67 <p>√97 ≅ 9.8488</p>

68 <p>So, √97 is greater than √96</p>

69 <p>Answer: √97 > √96 </p>

70 <h3>Explanation</h3>

71 <p>finding out the approximate values of √96 and √97 and comparing them </p>

72 <p>Well explained 👍</p>

73 <h3>Problem 4</h3>

74 <p>If y=√96, find y^2</p>

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

76 <p>firstly, y=√96= 9.79795897113</p>

77 <p>Now, squaring y, we get,</p>

78 <p> y2= (9.79795897113)2=96</p>

79 <p>or, y2=96</p>

80 <p>Answer : 96 </p>

81 <h3>Explanation</h3>

82 <p>squaring “y” which is same as squaring the value of √96 resulted to 96. </p>

83 <p>Well explained 👍</p>

84 <h3>Problem 5</h3>

85 <p>Find √96 / √48</p>

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

87 <p>√96/√48</p>

88 <p>= √(96/48)</p>

89 <p>= √2</p>

90 <p>= 1.414</p>

91 <p>Answer : 1.414 </p>

92 <h3>Explanation</h3>

93 <p>dividing the square root value of 96 with that of square root value of 48. </p>

94 <p>Well explained 👍</p>

95 <h2>FAQs on 96 Square Root</h2>

96 <h3>1. How to solve √95?</h3>

97 <p>√95 can be solved through various methods like Long Division Method, Prime Factorization Method or Approximation Method. The value is 9.7467943… </p>

98 <h3>2.Is 7 a factor of 96?</h3>

99 <p> No, 7 is not a factor of 96 </p>

100 <h3>3.Is 96 a perfect square or non-perfect square?</h3>

101 <p> 96 is a non-perfect square, since 96 =(9.79795897113)2. </p>

102 <h3>4.Is the square root of 96 a rational or irrational number?</h3>

103 <p>The square root of 96 is ±9.79795897113. So, 9.79795897113 is an<a>irrational number</a>, since it cannot be obtained by dividing two<a>integers</a>and cannot be written in the form p/q, where p and q are integers. </p>

104 <h3>5.What is the LCM of 96 and 404?</h3>

105 <p> 9696 is the LCM of 96 and 404, where 9696 is the smallest number that is a<a>multiple</a>of both 96 and 404, and it is also the number that both 96 and 404 divide into evenly. </p>

106 <h2>Important Glossaries for Square Root of 96</h2>

107 <ul><li><strong>Exponential form:</strong>An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent.Ex: 3 ⤬ 3 ⤬ 3 ⤬ 3 = 81 or, 34 = 81, where 3 is the base, 4 is the exponent </li>

108 </ul><ul><li><strong>Factorization:</strong>Expressing the given expression as a product of its factors Ex: 52=2 ⤬ 2 ⤬ 13 </li>

109 </ul><ul><li><strong>Prime Numbers :</strong>Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....</li>

110 </ul><ul><li><strong>Rational numbers and Irrational numbers:</strong>The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. </li>

111 </ul><ul><li><strong>perfect and non-perfect square numbers:</strong>Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :2, 8, 18 </li>

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

113 <p>▶</p>

114 <h2>Jaskaran Singh Saluja</h2>

115 <h3>About the Author</h3>

116 <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>

117 <h3>Fun Fact</h3>

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