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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 1168.</p>

4 <h2>What is the Square Root of 1168?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 1168 is not a<a>perfect square</a>. The square root of 1168 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1168, whereas (1168)^(1/2) in the exponential form. √1168 ≈ 34.175, 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 1168</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>and approximation methods are used. Let us now learn the following methods:</p>

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

9 <li>method Long division method </li>

10 <li>Approximation method</li>

11 </ul><h3>Square Root of 1168 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 1168 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 1168 Breaking it down, we get 2 x 2 x 2 x 2 x 73: 2^4 x 73^1</p>

14 <p><strong>Step 2:</strong>Now we have found the prime factors of 1168. The second step is to make pairs of those prime factors. Since 1168 is not a perfect square, the digits of the number can’t be grouped into pairs. Therefore, calculating 1168 using prime factorization is not possible to find an integer result.</p>

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17 <h3>Square Root of 1168 by Long Division Method</h3>

16 <h3>Square Root of 1168 by Long Division Method</h3>

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>

17 <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>

19 <p><strong>Step 1:</strong>To begin with, group the numbers from right to left. In the case of 1168, we group it as 68 and 11.</p>

18 <p><strong>Step 1:</strong>To begin with, group the numbers from right to left. In the case of 1168, we group it as 68 and 11.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is close to or<a>less than</a>11. We can say n is '3' because 3 x 3 = 9, which is lesser than 11. Now the<a>quotient</a>is 3, and after subtracting 9 from 11, the<a>remainder</a>is 2.</p>

19 <p><strong>Step 2:</strong>Now we need to find n whose square is close to or<a>less than</a>11. We can say n is '3' because 3 x 3 = 9, which is lesser than 11. Now the<a>quotient</a>is 3, and after subtracting 9 from 11, the<a>remainder</a>is 2.</p>

21 <p><strong>Step 3:</strong>Bring down 68, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the quotient, 3 + 3 = 6, which becomes the new divisor.</p>

20 <p><strong>Step 3:</strong>Bring down 68, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the quotient, 3 + 3 = 6, which becomes the new divisor.</p>

22 <p><strong>Step 4:</strong>We now have 26 as the new divisor. Find n such that 26n x n is less than or equal to 268.</p>

21 <p><strong>Step 4:</strong>We now have 26 as the new divisor. Find n such that 26n x n is less than or equal to 268.</p>

23 <p><strong>Step 5:</strong>Let's consider n as 9, then 26 x 9 = 234</p>

22 <p><strong>Step 5:</strong>Let's consider n as 9, then 26 x 9 = 234</p>

24 <p><strong>Step 6:</strong>Subtract 234 from 268; the difference is 34.</p>

23 <p><strong>Step 6:</strong>Subtract 234 from 268; the difference is 34.</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 remainder. The new dividend is 3400.</p>

24 <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 remainder. The new dividend is 3400.</p>

26 <p><strong>Step 8:</strong>The new divisor becomes 68 (from 260 + 8) because 681 x 5 approximates 3400.</p>

25 <p><strong>Step 8:</strong>The new divisor becomes 68 (from 260 + 8) because 681 x 5 approximates 3400.</p>

27 <p><strong>Step 9:</strong>Subtracting 3405 from 3400, we get a result of 5.</p>

26 <p><strong>Step 9:</strong>Subtracting 3405 from 3400, we get a result of 5.</p>

28 <p><strong>Step 10:</strong>Now the quotient is approximately 34.175.</p>

27 <p><strong>Step 10:</strong>Now the quotient is approximately 34.175.</p>

29 <h3>Square Root of 1168 by Approximation Method</h3>

28 <h3>Square Root of 1168 by Approximation Method</h3>

30 <p>The 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 1168 using the approximation method.</p>

29 <p>The 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 1168 using the approximation method.</p>

31 <p><strong>Step 1:</strong>Find the closest perfect squares around √1168. The closest perfect squares to 1168 are 1156 (34^2) and 1225 (35^2). √1168 falls between 34 and 35.</p>

30 <p><strong>Step 1:</strong>Find the closest perfect squares around √1168. The closest perfect squares to 1168 are 1156 (34^2) and 1225 (35^2). √1168 falls between 34 and 35.</p>

32 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (1168 - 1156) / (1225 - 1156) ≈ 0.175 Adding this to 34, we get 34 + 0.175 = 34.175. So, the square root of 1168 is approximately 34.175.</p>

31 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (1168 - 1156) / (1225 - 1156) ≈ 0.175 Adding this to 34, we get 34 + 0.175 = 34.175. So, the square root of 1168 is approximately 34.175.</p>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1168</h2>

32 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1168</h2>

34 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Here are some common mistakes and how to avoid them.</p>

33 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Here are some common mistakes and how to avoid them.</p>

34 + <h2>Download Worksheets</h2>

35 <h3>Problem 1</h3>

36 <p>Can you help Max find the area of a square box if its side length is given as √1168?</p>

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

38 <p>The area of the square is approximately 1363.89 square units.</p>

39 <h3>Explanation</h3>

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

41 <p>The side length is given as √1168.</p>

42 <p>Area of the square = side^2 = √1168 x √1168 ≈ 34.175 x 34.175 ≈ 1168.</p>

43 <p>Therefore, the area of the square box is approximately 1168 square units.</p>

44 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

46 <p>A square-shaped garden measuring 1168 square feet is built; if each of the sides is √1168, what will be the square feet of half of the garden?</p>

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

48 <p>584 square feet</p>

49 <h3>Explanation</h3>

50 <p>We can divide the given area by 2 since the garden is square-shaped.</p>

51 <p>Dividing 1168 by 2, we get 584.</p>

52 <p>So, half of the garden measures 584 square feet.</p>

53 <p>Well explained 👍</p>

54 <h3>Problem 3</h3>

55 <p>Calculate √1168 x 5.</p>

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

57 <p>Approx. 170.875</p>

58 <h3>Explanation</h3>

59 <p>The first step is to find the square root of 1168, which is approximately 34.175.</p>

60 <p>The second step is to multiply 34.175 by 5.</p>

61 <p>So, 34.175 x 5 ≈ 170.875.</p>

62 <p>Well explained 👍</p>

63 <h3>Problem 4</h3>

64 <p>What will be the square root of (1168 + 32)?</p>

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

66 <p>The square root is approximately 35.</p>

67 <h3>Explanation</h3>

68 <p>To find the square root, we need to find the sum of (1168 + 32). 1168 + 32 = 1200, and then √1200 ≈ 34.64.</p>

69 <p>Therefore, the square root of (1168 + 32) is approximately 34.64.</p>

70 <p>Well explained 👍</p>

71 <h3>Problem 5</h3>

72 <p>Find the perimeter of the rectangle if its length ‘l’ is √1168 units and the width ‘w’ is 38 units.</p>

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

74 <p>The perimeter of the rectangle is approximately 144.35 units.</p>

75 <h3>Explanation</h3>

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

77 <p>Perimeter = 2 × (√1168 + 38) = 2 × (34.175 + 38) ≈ 2 × 72.175 ≈ 144.35 units.</p>

78 <p>Well explained 👍</p>

79 <h2>FAQ on Square Root of 1168</h2>

80 <h3>1.What is √1168 in its simplest form?</h3>

81 <p>The prime factorization of 1168 is 2^4 x 73, so the simplest form of √1168 = √(2^4 x 73).</p>

82 <h3>2.Mention the factors of 1168.</h3>

83 <p>Factors of 1168 are 1, 2, 4, 8, 16, 73, 146, 292, 584, and 1168.</p>

84 <h3>3.Calculate the square of 1168.</h3>

85 <p>We get the square of 1168 by multiplying the number by itself, that is 1168 x 1168 = 1,364,224.</p>

86 <h3>4.Is 1168 a prime number?</h3>

87 <p>1168 is not a<a>prime number</a>, as it has more than two factors.</p>

88 <h3>5.1168 is divisible by?</h3>

89 <p>1168 has<a>multiple</a>factors; those are 1, 2, 4, 8, 16, 73, 146, 292, 584, and 1168.</p>

90 <h2>Important Glossaries for the Square Root of 1168</h2>

91 <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>

92 </ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.</li>

93 </ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, the positive square root is more prominent due to its uses in the real world. That is the reason it is also known as the principal square root.</li>

94 </ul><ul><li><strong>Approximation method:</strong>A method used to estimate the square root of non-perfect squares by finding the closest perfect squares around the number.</li>

95 </ul><ul><li><strong>Prime factorization:</strong>The process of breaking down a number into its basic prime number components, which is often used to simplify square roots.</li>

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

97 <p>▶</p>

98 <h2>Jaskaran Singh Saluja</h2>

99 <h3>About the Author</h3>

100 <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>

101 <h3>Fun Fact</h3>

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