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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 3969.</p>

4 <h2>What is the Square Root of 3969?</h2>

5 <p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 3969 is a<a>perfect square</a>. The square root of 3969 is expressed in both radical and exponential forms. In the radical form, it is expressed as √3969, whereas (3969)^(1/2) is the<a>exponential form</a>. √3969 = 63, 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 3969</h2>

7 <p>The<a>prime factorization</a>method is particularly useful for perfect square numbers. For non-perfect square numbers, the long-<a>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 3969 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 3969 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 3969 Breaking it down, we get 3 × 3 × 3 × 3 × 7 × 7:<a>3^4</a>× 7^2</p>

14 <p><strong>Step 2:</strong>Now we found out the prime factors of 3969. The second step is to make pairs of those prime factors. Since 3969 is a perfect square, we can group the digits in pairs. Step 3: Taking one number from each pair and multiplying, we get: 3 × 3 × 7 = 63</p>

15 <p>Therefore, the<a>square root</a>of 3969 is 63.</p>

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18 <h2>Square Root of 3969 by Long Division Method</h2>

17 <h2>Square Root of 3969 by Long Division Method</h2>

19 <p>The<a>long division</a>method is particularly used for non-perfect square numbers, but it can also be used for perfect squares. Let us now learn how to find the square root 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, but it can also be used for perfect squares. Let us now learn how to find the square root 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 3969, we need to group it as 69 and 39.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 3969, we need to group it as 69 and 39.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 39. We can say n is ‘6’ because 6 × 6 = 36, which is lesser than or equal to 39. Now the<a>quotient</a>is 6, and after subtracting 39 - 36, the<a>remainder</a>is 3.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 39. We can say n is ‘6’ because 6 × 6 = 36, which is lesser than or equal to 39. Now the<a>quotient</a>is 6, and after subtracting 39 - 36, the<a>remainder</a>is 3.</p>

22 <p><strong>Step 3:</strong>Now let us bring down 69, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 6 + 6, we get 12, which will be our new divisor.</p>

21 <p><strong>Step 3:</strong>Now let us bring down 69, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 6 + 6, we get 12, 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 12n as the new divisor, and 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 12n as the new divisor, and we need to find the value of n.</p>

24 <p><strong>Step 5:</strong>The next step is finding 12n × n ≤ 369. Let us consider n as 3, now 12 × 3 × 3 = 369.</p>

23 <p><strong>Step 5:</strong>The next step is finding 12n × n ≤ 369. Let us consider n as 3, now 12 × 3 × 3 = 369.</p>

25 <p><strong>Step 6:</strong>Subtract 369 from 369, and the difference is 0, and the quotient is 63.</p>

24 <p><strong>Step 6:</strong>Subtract 369 from 369, and the difference is 0, and the quotient is 63.</p>

26 <p>Since the remainder is zero, the square root of 3969 is 63.</p>

25 <p>Since the remainder is zero, the square root of 3969 is 63.</p>

27 <h2>Square Root of 3969 by Approximation Method</h2>

26 <h2>Square Root of 3969 by Approximation Method</h2>

28 <p>The approximation method is another way for finding square roots, especially useful for non-perfect squares, but can also verify perfect squares. Now let us learn how to find the square root of 3969 using the approximation method.</p>

27 <p>The approximation method is another way for finding square roots, especially useful for non-perfect squares, but can also verify perfect squares. Now let us learn how to find the square root of 3969 using the approximation method.</p>

29 <p><strong>Step 1:</strong>Now we have to find the closest perfect square of √3969. The closest perfect squares are 3600 (60^2) and 4096 (64^2). √3969 falls between 60 and 64, but since 3969 is a perfect square, we know the exact square root is 63.</p>

28 <p><strong>Step 1:</strong>Now we have to find the closest perfect square of √3969. The closest perfect squares are 3600 (60^2) and 4096 (64^2). √3969 falls between 60 and 64, but since 3969 is a perfect square, we know the exact square root is 63.</p>

30 <p><strong>Step 2:</strong>Since we've identified 3969 as a perfect square, there is no need for further approximation. We know that √3969 = 63.</p>

29 <p><strong>Step 2:</strong>Since we've identified 3969 as a perfect square, there is no need for further approximation. We know that √3969 = 63.</p>

31 <h2>Common Mistakes and How to Avoid Them in the Square Root of 3969</h2>

30 <h2>Common Mistakes and How to Avoid Them in the Square Root of 3969</h2>

32 <p>Students do make mistakes while finding the square root, like 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>

31 <p>Students do make mistakes while finding the square root, like 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>

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33 <h3>Problem 1</h3>

34 <p>Can you help Max find the area of a square box if its side length is given as √3249?</p>

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

36 <p>The area of the square is 3249 square units.</p>

37 <h3>Explanation</h3>

38 <p>The area of the square = side².</p>

39 <p>The side length is given as √3249.</p>

40 <p>Area of the square = side² = √3249 × √3249 = 57 × 57 = 3249.</p>

41 <p>Therefore, the area of the square box is 3249 square units.</p>

42 <p>Well explained 👍</p>

43 <h3>Problem 2</h3>

44 <p>A square-shaped building measuring 3969 square feet is built; if each of the sides is √3969, what will be the square feet of half of the building?</p>

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

46 <p>1984.5 square feet</p>

47 <h3>Explanation</h3>

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

49 <p>Dividing 3969 by 2 = 1984.5.</p>

50 <p>So half of the building measures 1984.5 square feet.</p>

51 <p>Well explained 👍</p>

52 <h3>Problem 3</h3>

53 <p>Calculate √3969 × 5.</p>

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

55 <p>315</p>

56 <h3>Explanation</h3>

57 <p>The first step is to find the square root of 3969, which is 63.</p>

58 <p>The second step is to multiply 63 with 5.</p>

59 <p>So 63 × 5 = 315.</p>

60 <p>Well explained 👍</p>

61 <h3>Problem 4</h3>

62 <p>What will be the square root of (3249 + 720)?</p>

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

64 <p>The square root is 69.</p>

65 <h3>Explanation</h3>

66 <p>To find the square root, we need to find the sum of (3249 + 720).</p>

67 <p>3249 + 720 = 3969, and then √3969 = 63.</p>

68 <p>Therefore, the square root of (3249 + 720) is ±63.</p>

69 <p>Well explained 👍</p>

70 <h3>Problem 5</h3>

71 <p>Find the perimeter of the rectangle if its length ‘l’ is √3249 units and the width ‘w’ is 38 units.</p>

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

73 <p>We find the perimeter of the rectangle as 190 units.</p>

74 <h3>Explanation</h3>

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

76 <p>Perimeter = 2 × (√3249 + 38)</p>

77 <p>= 2 × (57 + 38)</p>

78 <p>= 2 × 95</p>

79 <p>= 190 units.</p>

80 <p>Well explained 👍</p>

81 <h2>FAQ on Square Root of 3969</h2>

82 <h3>1.What is √3969 in its simplest form?</h3>

83 <p>The prime factorization of 3969 is 3 × 3 × 3 × 3 × 7 × 7, so the simplest form of √3969 = √(3^4 × 7^2) = 63.</p>

84 <h3>2.Mention the factors of 3969.</h3>

85 <p>Factors of 3969 are 1, 3, 9, 21, 27, 63, 189, 441, 1323, 3969.</p>

86 <h3>3.Calculate the square of 3969.</h3>

87 <p>We get the square of 3969 by multiplying the number by itself, that is 3969 × 3969 = 15,747,561.</p>

88 <h3>4.Is 3969 a prime number?</h3>

89 <p>3969 is not a<a>prime number</a>, as it has more than two factors.</p>

90 <h3>5.3969 is divisible by?</h3>

91 <p>3969 has many factors; those are 1, 3, 9, 21, 27, 63, 189, 441, 1323, 3969.</p>

92 <h2>Important Glossaries for the Square Root of 3969</h2>

93 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 8² = 64, and the inverse of the square is the square root, that is √64 = 8. </li>

94 <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>

95 <li><strong>Perfect square:</strong>A perfect square is a number that has an integer as its square root. For example, 64 is a perfect square because its square root is 8. </li>

96 <li><strong>Prime factorization:</strong>Prime factorization is the process of expressing a number as the product of its prime factors. </li>

97 <li><strong>Long division method:</strong>A method used to find the square root of a number by dividing it into smaller, more manageable parts.</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>