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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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1368.</p>

4 <h2>What is the Square Root of 1368?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 1368 is not a<a>perfect square</a>. The square root of 1368 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1368, whereas (1368)^(1/2) in the exponential form. √1368 ≈ 36.9858, 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 1368</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 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 1368 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 1368 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 1368.</p>

14 <p>Breaking it down, we get 2 × 2 × 2 × 3 × 3 × 19: 2^3 × 3^2 × 19</p>

15 <p><strong>Step 2:</strong>Now that we have found the prime factors of 1368, the second step is to make pairs of those prime factors. Since 1368 is not a perfect square, the digits of the number can’t be fully grouped in pairs. Therefore, calculating 1368 using prime factorization is limited in providing an exact integer result.</p>

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18 <h2>Square Root of 1368 by Long Division Method</h2>

17 <h2>Square Root of 1368 by Long Division Method</h2>

19 <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<a>square root</a>using the long division method, step by step.</p>

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<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 1368, we need to group it as 68 and 13.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1368, we need to group it as 68 and 13.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 13. We can say n is '3' because 3 × 3 = 9 is less than or equal to 13. Now the<a>quotient</a>is 3, after subtracting 9 from 13, the<a>remainder</a>is 4.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 13. We can say n is '3' because 3 × 3 = 9 is less than or equal to 13. Now the<a>quotient</a>is 3, after subtracting 9 from 13, the<a>remainder</a>is 4.</p>

22 <p><strong>Step 3:</strong>Bring down 68, making the new<a>dividend</a>468. Add the old<a>divisor</a>with the same number: 3 + 3 = 6, which will be our new divisor.</p>

21 <p><strong>Step 3:</strong>Bring down 68, making the new<a>dividend</a>468. Add the old<a>divisor</a>with the same number: 3 + 3 = 6, which will be our new divisor.</p>

23 <p><strong>Step 4:</strong>The new divisor is 6n. We need to find n such that 6n × n ≤ 468. Let n be 7, then 67 × 7 = 469 which is slightly more than 468. Let's use n = 6, 66 × 6 = 396.</p>

22 <p><strong>Step 4:</strong>The new divisor is 6n. We need to find n such that 6n × n ≤ 468. Let n be 7, then 67 × 7 = 469 which is slightly more than 468. Let's use n = 6, 66 × 6 = 396.</p>

24 <p><strong>Step 5:</strong>Subtract 396 from 468, the difference is 72, and the quotient is 36.</p>

23 <p><strong>Step 5:</strong>Subtract 396 from 468, the difference is 72, and the quotient is 36.</p>

25 <p><strong>Step 6:</strong>Add a decimal point to continue the division and bring down two zeros to the remainder, making it 7200.</p>

24 <p><strong>Step 6:</strong>Add a decimal point to continue the division and bring down two zeros to the remainder, making it 7200.</p>

26 <p><strong>Step 7:</strong>Find the next divisor. Use the quotient 369, so 369n ≤ 7200. Find suitable n; let's say n = 1, 369 × 1 = 369.</p>

25 <p><strong>Step 7:</strong>Find the next divisor. Use the quotient 369, so 369n ≤ 7200. Find suitable n; let's say n = 1, 369 × 1 = 369.</p>

27 <p><strong>Step 8:</strong>Continue the division until the desired accuracy is reached. So the square root of √1368 is approximately 36.98.</p>

26 <p><strong>Step 8:</strong>Continue the division until the desired accuracy is reached. So the square root of √1368 is approximately 36.98.</p>

28 <h2>Square Root of 1368 by Approximation Method</h2>

27 <h2>Square Root of 1368 by Approximation Method</h2>

29 <p>The approximation method is another method for finding 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 1368 using the approximation method.</p>

28 <p>The approximation method is another method for finding 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 1368 using the approximation method.</p>

30 <p><strong>Step 1:</strong>Find the closest perfect squares around √1368. The smallest perfect square less than 1368 is 1296 (36^2) and the largest perfect square more than 1368 is 1444 (38^2). √1368 falls between 36 and 38.</p>

29 <p><strong>Step 1:</strong>Find the closest perfect squares around √1368. The smallest perfect square less than 1368 is 1296 (36^2) and the largest perfect square more than 1368 is 1444 (38^2). √1368 falls between 36 and 38.</p>

31 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smaller perfect square) ÷ (larger perfect square - smaller perfect square). Using the formula: (1368 - 1296) ÷ (1444 - 1296) = 72 ÷ 148 ≈ 0.486 Add this<a>decimal</a>to the lower integer square root: 36 + 0.486 = 36.486, so the square root of 1368 is approximately 36.49.</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: (1368 - 1296) ÷ (1444 - 1296) = 72 ÷ 148 ≈ 0.486 Add this<a>decimal</a>to the lower integer square root: 36 + 0.486 = 36.486, so the square root of 1368 is approximately 36.49.</p>

32 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1368</h2>

31 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1368</h2>

33 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>

32 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, etc. Now let us look at a few of those mistakes that students tend to make 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 √1368?</p>

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

37 <p>The area of the square is approximately 1368 square units.</p>

38 <h3>Explanation</h3>

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

40 <p>The side length is given as √1368.</p>

41 <p>Area of the square = side^2 = √1368 × √1368 = 1368.</p>

42 <p>Therefore, the area of the square box is approximately 1368 square units.</p>

43 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

45 <p>A square-shaped building measuring 1368 square feet is built; if each of the sides is √1368, what will be the square feet of half of the building?</p>

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

47 <p>684 square feet</p>

48 <h3>Explanation</h3>

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

50 <p>Dividing 1368 by 2 = we get 684.</p>

51 <p>So half of the building measures 684 square feet.</p>

52 <p>Well explained 👍</p>

53 <h3>Problem 3</h3>

54 <p>Calculate √1368 × 5.</p>

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

56 <p>Approximately 184.93</p>

57 <h3>Explanation</h3>

58 <p>The first step is to find the square root of 1368, which is approximately 36.98.</p>

59 <p>The second step is to multiply 36.98 by 5.</p>

60 <p>So, 36.98 × 5 ≈ 184.93</p>

61 <p>Well explained 👍</p>

62 <h3>Problem 4</h3>

63 <p>What will be the square root of (1368 + 32)?</p>

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

65 <p>The square root is approximately 38.</p>

66 <h3>Explanation</h3>

67 <p>To find the square root, we need to find the sum of (1368 + 32). 1368 + 32 = 1400, and then √1400 ≈ 37.42.</p>

68 <p>Therefore, the square root of (1368 + 32) is approximately 37.42.</p>

69 <p>Well explained 👍</p>

70 <h3>Problem 5</h3>

71 <p>Find the perimeter of the rectangle if its length ‘l’ is √1368 units and the width ‘w’ is 40 units.</p>

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

73 <p>The perimeter of the rectangle is approximately 153.96 units.</p>

74 <h3>Explanation</h3>

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

76 <p>Perimeter = 2 × (√1368 + 40) = 2 × (36.98 + 40) = 2 × 76.98 ≈ 153.96 units.</p>

77 <p>Well explained 👍</p>

78 <h2>FAQ on Square Root of 1368</h2>

79 <h3>1.What is √1368 in its simplest form?</h3>

80 <p>The prime factorization of 1368 is 2 × 2 × 2 × 3 × 3 × 19. The simplest form of √1368 = √(2 × 2 × 2 × 3 × 3 × 19).</p>

81 <h3>2.Mention the factors of 1368.</h3>

82 <p>Factors of 1368 are 1, 2, 3, 4, 6, 8, 9, 12, 19, 24, 27, 36, 38, 57, 72, 76, 114, 152, 171, 228, 342, 456, 684, and 1368.</p>

83 <h3>3.Calculate the square of 1368.</h3>

84 <p>We get the square of 1368 by multiplying the number by itself, that is 1368 × 1368 = 1,872,624.</p>

85 <h3>4.Is 1368 a prime number?</h3>

86 <p>1368 is not a<a>prime number</a>, as it has more than two factors.</p>

87 <h3>5.1368 is divisible by?</h3>

88 <p>1368 has many factors; those are 1, 2, 3, 4, 6, 8, 9, 12, 19, 24, 27, 36, 38, 57, 72, 76, 114, 152, 171, 228, 342, 456, 684, and 1368.</p>

89 <h2>Important Glossaries for the Square Root of 1368</h2>

90 <ul><li><strong>Square root</strong>: A square root of a number is a value that, when multiplied by itself, gives the original number. Example: 6^2 = 36, and the square root is √36 = 6.</li>

91 </ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be expressed as a simple fraction; its decimal goes on forever without repeating.</li>

92 </ul><ul><li><strong>Approximation</strong>: The process of finding a value that is close enough to the correct answer, usually within a specified tolerance.</li>

93 </ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. Example: 36 is a perfect square because it is 6^2.</li>

94 </ul><ul><li><strong>Prime factorization:</strong>Expressing a number as the product of its prime factors. Example: The prime factorization of 1368 is 2^3 × 3^2 × 19.</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>