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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 168.</p>

4 <h2>What is the square root of 168?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 168 is not a<a>perfect square</a>. The square root of 168 is expressed in both radical and<a>exponential form</a>. In the radical form it is expressed as, √168 , whereas (168)1/2 in the exponential form. √168 = 12.96148, 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>

6 <h2>Finding the square root of 168</h2>

7 <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</p>

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

9 <li>Long division method </li>

10 <li>Approximation method </li>

11 </ul><h3>Square Root of 168 by Prime Factorization Method</h3>

12 <p>The<a>product</a>of prime<a>factors</a>is the Prime factorization of a number. Now let us look at how 168 is broken down into its prime factors </p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 168</p>

14 <p>Breaking it down, we get 2 x 2 x 2 x 3 x 7: 23 x 31 x 71</p>

15 <p><strong>Step 2:</strong>Now we found out the prime factors of 168. The second step is to make pairs of those prime factors. Since 168 is not a perfect square, therefore the digits of the number can’t be grouped in pair. Therefore, calculating 168 using prime factorization is impossible. </p>

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18 <h2>Square Root of 168 by Long Division Method</h2>

17 <h2>Square Root of 168 by Long Division Method</h2>

19 <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>

18 <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>

20 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 168, we need to group it as 68 and 1. </p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 168, we need to group it as 68 and 1. </p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is 1. We can say n as ‘1’ because 1 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>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is 1. We can say n as ‘1’ because 1 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>

22 <p><strong>Step 3:</strong>Now let us bring down 68 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>

21 <p><strong>Step 3:</strong>Now let us bring down 68 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>

23 <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>

22 <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>

24 <p><strong>Step 5:</strong>The next step is finding 2 n × n ≤ 68 let us consider n as 2, now 22 x 2 = 44</p>

23 <p><strong>Step 5:</strong>The next step is finding 2 n × n ≤ 68 let us consider n as 2, now 22 x 2 = 44</p>

25 <p><strong>Step 6:</strong>Subtract 68 from 44 the difference is 24, and the quotient is 12</p>

24 <p><strong>Step 6:</strong>Subtract 68 from 44 the difference is 24, and the quotient is 12</p>

26 <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 zeroes to the dividend. Now the new dividend is 2400.</p>

25 <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 zeroes to the dividend. Now the new dividend is 2400.</p>

27 <p><strong>Step 8:</strong>Now we need to find the new divisor that is 9 because 249 ✖ 9 = 2241 </p>

26 <p><strong>Step 8:</strong>Now we need to find the new divisor that is 9 because 249 ✖ 9 = 2241 </p>

28 <p><strong>Step 9:</strong>Subtracting 2241 from 2400 we get the result 159.</p>

27 <p><strong>Step 9:</strong>Subtracting 2241 from 2400 we get the result 159.</p>

29 <p><strong>Step 10:</strong>Now the quotient is 12.9</p>

28 <p><strong>Step 10:</strong>Now the quotient is 12.9</p>

30 <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>

29 <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>

31 <p>So the square root of √168 is 12. 96</p>

30 <p>So the square root of √168 is 12. 96</p>

32 <h2>Square root of 168 by approximation method</h2>

31 <h2>Square root of 168 by approximation method</h2>

33 <p>Approximation method is another method for finding the 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 168 using the approximation method</p>

32 <p>Approximation method is another method for finding the 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 168 using the approximation method</p>

34 <p><strong>Step 1:</strong>Now we have to find the closest perfect square of √168 </p>

33 <p><strong>Step 1:</strong>Now we have to find the closest perfect square of √168 </p>

35 <p>The smallest perfect square of 168 is 144 and the largest perfect square of 168 is 169. √168 falls somewhere between 12 and 13</p>

34 <p>The smallest perfect square of 168 is 144 and the largest perfect square of 168 is 169. √168 falls somewhere between 12 and 13</p>

36 <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)</p>

35 <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)</p>

37 <p>Going by the formula (168 - 144) ÷ (169-144) = 0.96</p>

36 <p>Going by the formula (168 - 144) ÷ (169-144) = 0.96</p>

38 <p>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 which is 12 + 0.96 = 12.96, so the square root of 168 is 12.96</p>

37 <p>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 which is 12 + 0.96 = 12.96, so the square root of 168 is 12.96</p>

39 <p>12 + 0.96 = 12.96, so the square root of 168 is 12.96 </p>

38 <p>12 + 0.96 = 12.96, so the square root of 168 is 12.96 </p>

40 <h2>Common Mistakes and How to Avoid Them in the Square Root of 168</h2>

39 <h2>Common Mistakes and How to Avoid Them in the Square Root of 168</h2>

41 <p>Students do make mistakes while finding the square root, likewise 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>

40 <p>Students do make mistakes while finding the square root, likewise 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>

41 + <h2>Download Worksheets</h2>

42 <h3>Problem 1</h3>

43 <p>A square-shaped room is 168 square feet, calculate the length of each side of the room.</p>

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

45 <p>The length of each side of the room is 12.96 square feet </p>

46 <h3>Explanation</h3>

47 <p> To calculate the length of the side of the room, we need to calculate the square root of 168</p>

48 <p>√168 = 12.96</p>

49 <p>This tells us the length of the side of the square room is 12.96 square feet </p>

50 <p>Well explained 👍</p>

51 <h3>Problem 2</h3>

52 <p>A square shaped building measuring 168 square feet is built; if each sides is √168 , what will be the square feet of half of the building?</p>

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

54 <p> 84 square meters </p>

55 <h3>Explanation</h3>

56 <p>We can just divide given area by 2 as the building is square shaped</p>

57 <p>Dividing 168 by 2 = we get 84</p>

58 <p>So half of the building measures 84 square meters </p>

59 <p>Well explained 👍</p>

60 <h3>Problem 3</h3>

61 <p>Calculate √168 x √5?</p>

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

63 <p>64.8 </p>

64 <h3>Explanation</h3>

65 <p> The first step is to find the square root of 168 which is 12.96, the second step is to multiply 12.96 with 5</p>

66 <p>So 12.96 x 5 = 64.8 </p>

67 <p>Well explained 👍</p>

68 <h3>Problem 4</h3>

69 <p>√168 Can this be expressed as a fraction?</p>

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

71 <p>Yes, it can be expressed as a fraction</p>

72 <h3>Explanation</h3>

73 <p>we can express the square root of 168 as a fraction, as it is a irrational number</p>

74 <p>Well explained 👍</p>

75 <h3>Problem 5</h3>

76 <p>Identify the length of the side of the square table if the area is 168 square feet.</p>

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

78 <p>12.96 square feet </p>

79 <h3>Explanation</h3>

80 <p>To calculate the side of the table we need to identify the square root of 168 that is 168 = 12.96</p>

81 <p>Well explained 👍</p>

82 <h2>FAQ on square root of 168</h2>

83 <h3>1.What is √168 in its simplest form?</h3>

84 <p> The prime factorization of 168 is 2 x 2 x 2 x 3 x 7 so the simplest form of √168 = √(2 x 2 x 2 x 3 x 7) </p>

85 <h3>2.Mention the factors of 168.</h3>

86 <p>Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168</p>

87 <h3>3.Calculate the square of 168.</h3>

88 <p>We get the square of 168 by multiplying the number by itself, that is 168 x 168 = 28224 </p>

89 <h3>4.Is 168 a prime number?</h3>

90 <h3>5.168 is divisible by?</h3>

91 <p>168 has many factors; those are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.</p>

92 <h2>Important Glossaries for the Square Root of 168</h2>

93 <ul><li><strong>Square root:</strong>A square root is the Inverse of a square .Example: 42 =16 and the inverse of square is square root that is √ 16 = 4</li>

94 </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>

95 </ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots, however, it is always a 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>

96 </ul><ul><li><strong>Integers:</strong>The combination of whole numbers and negative numbers are integers for example: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6,7………….are integers</li>

97 </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>

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

99 <p>▶</p>

100 <h2>Jaskaran Singh Saluja</h2>

101 <h3>About the Author</h3>

102 <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>

103 <h3>Fun Fact</h3>

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