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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 1296.</p>

4 <h2>What is the Square Root of 1296?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 1296 is a<a>perfect square</a>. The square root of 1296 can be expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √1296, whereas (1296)^(1/2) in exponential form. √1296 = 36, 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 1296</h2>

7 <p>The<a>prime factorization</a>method is 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 1296 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 1296 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 1296</p>

14 <p>Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3: 2^4 x<a>3^4</a></p>

15 <p><strong>Step 2:</strong>Now we found out the prime factors of 1296. Since 1296 is a perfect square, we can pair the prime factors. Therefore, √1296 = (2^2 x 3^2) = 36.</p>

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18 <h2>Square Root of 1296 by Long Division Method</h2>

17 <h2>Square Root of 1296 by Long Division Method</h2>

19 <p>The long<a>division</a>method is particularly used for non-perfect square numbers, but it can also verify perfect squares. 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, but it can also verify perfect squares. 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 1296, we group it as 12 and 96.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1296, we group it as 12 and 96.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 12. We can say n is ‘3’ because 3 x 3 = 9, which is less than 12. The<a>quotient</a>is 3, and the<a>remainder</a>is 12 - 9 = 3.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 12. We can say n is ‘3’ because 3 x 3 = 9, which is less than 12. The<a>quotient</a>is 3, and the<a>remainder</a>is 12 - 9 = 3.</p>

22 <p><strong>Step 3</strong>: Now bring down 96, making the new<a>dividend</a>396. Double the quotient (3) to get 6, which becomes part of our new<a>divisor</a>.</p>

21 <p><strong>Step 3</strong>: Now bring down 96, making the new<a>dividend</a>396. Double the quotient (3) to get 6, which becomes part of our new<a>divisor</a>.</p>

23 <p><strong>Step 4:</strong>Find a digit x such that 6x x x is less than or equal to 396. Here, x is 6, because 66 x 6 = 396.</p>

22 <p><strong>Step 4:</strong>Find a digit x such that 6x x x is less than or equal to 396. Here, x is 6, because 66 x 6 = 396.</p>

24 <p><strong>Step 5:</strong>Subtract 396 from 396 to get a remainder of 0. The quotient is 36, which is the square root of 1296.</p>

23 <p><strong>Step 5:</strong>Subtract 396 from 396 to get a remainder of 0. The quotient is 36, which is the square root of 1296.</p>

25 <h2>Square Root of 1296 by Approximation Method</h2>

24 <h2>Square Root of 1296 by Approximation Method</h2>

26 <p>The approximation method is another method for finding square roots, especially for non-perfect squares. It is not necessary for perfect square 1296, but let's apply it for understanding.</p>

25 <p>The approximation method is another method for finding square roots, especially for non-perfect squares. It is not necessary for perfect square 1296, but let's apply it for understanding.</p>

27 <p><strong>Step 1:</strong>We have to find the closest perfect squares around √1296. Since 1296 is a perfect square, it's exactly 36.</p>

26 <p><strong>Step 1:</strong>We have to find the closest perfect squares around √1296. Since 1296 is a perfect square, it's exactly 36.</p>

28 <p><strong>Step 2:</strong>Using the approximation method is unnecessary here, as the perfect square of 1296 is exactly 36.</p>

27 <p><strong>Step 2:</strong>Using the approximation method is unnecessary here, as the perfect square of 1296 is exactly 36.</p>

29 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1296</h2>

28 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1296</h2>

30 <p>Students do 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>

29 <p>Students do 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>

30 + <h2>Download Worksheets</h2>

31 <h3>Problem 1</h3>

32 <p>Can you help Max find the area of a square box if its side length is given as √169?</p>

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

34 <p>The area of the square is 169 square units.</p>

35 <h3>Explanation</h3>

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

37 <p>The side length is given as √169.</p>

38 <p>Area of the square = side^2 = √169 x √169 = 13 x 13 = 169.</p>

39 <p>Therefore, the area of the square box is 169 square units.</p>

40 <p>Well explained 👍</p>

41 <h3>Problem 2</h3>

42 <p>A square-shaped building measuring 1296 square feet is built; if each of the sides is √1296, what will be the square feet of half of the building?</p>

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

44 <p>648 square feet</p>

45 <h3>Explanation</h3>

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

47 <p>Dividing 1296 by 2, we get 648.</p>

48 <p>So half of the building measures 648 square feet.</p>

49 <p>Well explained 👍</p>

50 <h3>Problem 3</h3>

51 <p>Calculate √1296 x 5.</p>

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

53 <p>180</p>

54 <h3>Explanation</h3>

55 <p>The first step is to find the square root of 1296, which is 36.</p>

56 <p>The second step is to multiply 36 by 5.</p>

57 <p>So, 36 x 5 = 180.</p>

58 <p>Well explained 👍</p>

59 <h3>Problem 4</h3>

60 <p>What will be the square root of (144 + 9)?</p>

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

62 <p>The square root is 12.</p>

63 <h3>Explanation</h3>

64 <p>To find the square root, we need to find the sum of (144 + 9). 144 + 9 = 153, and then √153 cannot be simplified as a perfect square.</p>

65 <p>Therefore, the square root of (144 + 9) is approximately 12.37 (for simplicity, the nearest integer is 12).</p>

66 <p>Well explained 👍</p>

67 <h3>Problem 5</h3>

68 <p>Find the perimeter of a rectangle if its length ‘l’ is √256 units and the width ‘w’ is 40 units.</p>

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

70 <p>We find the perimeter of the rectangle as 96 units.</p>

71 <h3>Explanation</h3>

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

73 <p>Perimeter = 2 × (√256 + 40) = 2 × (16 + 40) = 2 × 56 = 112 units.</p>

74 <p>Well explained 👍</p>

75 <h2>FAQ on Square Root of 1296</h2>

76 <h3>1.What is √1296 in its simplest form?</h3>

77 <p>The prime factorization of 1296 is 2^4 x 3^4, so the simplest form of √1296 = √(2^4 x 3^4) = 36.</p>

78 <h3>2.Mention the factors of 1296.</h3>

79 <p>Factors of 1296 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648, and 1296.</p>

80 <h3>3.Calculate the square of 1296.</h3>

81 <p>We get the square of 1296 by multiplying the number by itself, that is 1296 x 1296 = 1,679,616.</p>

82 <h3>4.Is 1296 a prime number?</h3>

83 <p>1296 is not a<a>prime number</a>, as it has more than two factors.</p>

84 <h3>5.1296 is divisible by?</h3>

85 <p>1296 has many factors; those are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648, and 1296.</p>

86 <h2>Important Glossaries for the Square Root of 1296</h2>

87 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 6^2 = 36 and the inverse of the square is the square root, which is √36 = 6.</li>

88 </ul><ul><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>

89 </ul><ul><li><strong>Perfect square:</strong>A perfect square is an integer that is the square of an integer. For example, 36 is a perfect square because it is 6^2.</li>

90 </ul><ul><li><strong>Dividend:</strong>In division, the number that is being divided is called the dividend. For example, in 1296 ÷ 36 = 36, 1296 is the dividend.</li>

91 </ul><ul><li><strong>Divisor:</strong>In division, the number by which the dividend is divided is called the divisor. For example, in 1296 ÷ 36 = 36, 36 is the divisor.</li>

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

93 <p>▶</p>

94 <h2>Jaskaran Singh Saluja</h2>

95 <h3>About the Author</h3>

96 <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>

97 <h3>Fun Fact</h3>

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