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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 3364.</p>

4 <h2>What is the Square Root of 3364?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 3364 is a<a>perfect square</a>. The square root of 3364 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √3364, whereas (3364)^(1/2) in the exponential form. √3364 = 58, 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 3364</h2>

7 <p>The<a>prime factorization</a>method is used 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><h3>Square Root of 3364 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 3364 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 3364 Breaking it down, we get 2 x 2 x 29 x 29: 2^2 x 29^2</p>

14 <p><strong>Step 2:</strong>Now we found out the prime factors of 3364. The second step is to make pairs of those prime factors. Since 3364 is a perfect square, the digits of the number can be grouped in pairs. Therefore, √3364 = 2 x 29 = 58.</p>

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17 <h3>Square Root of 3364 by Long Division Method</h3>

16 <h3>Square Root of 3364 by Long Division Method</h3>

18 <p>The<a>long division</a>method is particularly used for both perfect and 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 both perfect and 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, we need to group the numbers from right to left. In the case of 3364, we group it as 33 and 64.</p>

18 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 3364, we group it as 33 and 64.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 33. We can say n is ‘5’ because 5 x 5 = 25 is<a>less than</a>33. The<a>quotient</a>is 5, and the<a>remainder</a>is 33 - 25 = 8.</p>

19 <p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 33. We can say n is ‘5’ because 5 x 5 = 25 is<a>less than</a>33. The<a>quotient</a>is 5, and the<a>remainder</a>is 33 - 25 = 8.</p>

21 <p><strong>Step 3:</strong>Bring down 64, making the new<a>dividend</a>864. Add the old<a>divisor</a>with the same number, 5 + 5, to get 10, which becomes the new divisor.</p>

20 <p><strong>Step 3:</strong>Bring down 64, making the new<a>dividend</a>864. Add the old<a>divisor</a>with the same number, 5 + 5, to get 10, which becomes the new divisor.</p>

22 <p><strong>Step 4:</strong>Find n such that 10n x n ≤ 864. Consider n as 8, so 108 x 8 = 864.</p>

21 <p><strong>Step 4:</strong>Find n such that 10n x n ≤ 864. Consider n as 8, so 108 x 8 = 864.</p>

23 <p><strong>Step 5</strong>: Subtract 864 from 864; the remainder is 0. So, the square root of √3364 is 58.</p>

22 <p><strong>Step 5</strong>: Subtract 864 from 864; the remainder is 0. So, the square root of √3364 is 58.</p>

24 <h3>Square Root of 3364 by Approximation Method</h3>

23 <h3>Square Root of 3364 by Approximation Method</h3>

25 <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 3364 using the approximation method.</p>

24 <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 3364 using the approximation method.</p>

26 <p><strong>Step 1:</strong>Identify the closest perfect square of √3364. 3364 is a perfect square, so the closest perfect square is itself. √3364 falls exactly on 58.</p>

25 <p><strong>Step 1:</strong>Identify the closest perfect square of √3364. 3364 is a perfect square, so the closest perfect square is itself. √3364 falls exactly on 58.</p>

27 <p><strong>Step 2:</strong>Since 3364 is a perfect square, no further approximation is necessary. √3364 = 58.</p>

26 <p><strong>Step 2:</strong>Since 3364 is a perfect square, no further approximation is necessary. √3364 = 58.</p>

28 <h2>Common Mistakes and How to Avoid Them in the Square Root of 3364</h2>

27 <h2>Common Mistakes and How to Avoid Them in the Square Root of 3364</h2>

29 <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>

28 <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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30 <h3>Problem 1</h3>

31 <p>Can you help Max find the area of a square box if its side length is given as √3364?</p>

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

33 <p>The area of the square is 3364 square units.</p>

34 <h3>Explanation</h3>

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

36 <p>The side length is given as √3364.</p>

37 <p>Area of the square = side^2 = √3364 x √3364 = 58 x 58 = 3364.</p>

38 <p>Therefore, the area of the square box is 3364 square units.</p>

39 <p>Well explained 👍</p>

40 <h3>Problem 2</h3>

41 <p>A square-shaped building measuring 3364 square feet is built; if each of the sides is √3364, what will be the square feet of half of the building?</p>

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

43 <p>1682 square feet</p>

44 <h3>Explanation</h3>

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

46 <p>Dividing 3364 by 2 = 1682.</p>

47 <p>So half of the building measures 1682 square feet.</p>

48 <p>Well explained 👍</p>

49 <h3>Problem 3</h3>

50 <p>Calculate √3364 x 5.</p>

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

52 <p>290</p>

53 <h3>Explanation</h3>

54 <p>The first step is to find the square root of 3364, which is 58; the second step is to multiply 58 with 5. So, 58 x 5 = 290.</p>

55 <p>Well explained 👍</p>

56 <h3>Problem 4</h3>

57 <p>What will be the square root of (324 + 40)?</p>

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

59 <p>The square root is 19.</p>

60 <h3>Explanation</h3>

61 <p>To find the square root, we need to find the sum of (324 + 40).</p>

62 <p>324 + 40 = 364, and then √364 ≈ 19.052.</p>

63 <p>Therefore, the square root of (324 + 40) is approximately ±19.052.</p>

64 <p>Well explained 👍</p>

65 <h3>Problem 5</h3>

66 <p>Find the perimeter of the rectangle if its length ‘l’ is √3364 units and the width ‘w’ is 40 units.</p>

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

68 <p>We find the perimeter of the rectangle as 196 units.</p>

69 <h3>Explanation</h3>

70 <p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√3364 + 40) = 2 × (58 + 40) = 2 × 98 = 196 units.</p>

71 <p>Well explained 👍</p>

72 <h2>FAQ on Square Root of 3364</h2>

73 <h3>1.What is √3364 in its simplest form?</h3>

74 <p>The prime factorization of 3364 is 2^2 x 29^2, so the simplest form of √3364 = 2 x 29 = 58.</p>

75 <h3>2.Mention the factors of 3364.</h3>

76 <p>Factors of 3364 are 1, 2, 4, 29, 58, 116, 841, 1682, and 3364.</p>

77 <h3>3.Calculate the square of 3364.</h3>

78 <p>We get the square of 3364 by multiplying the number by itself, that is 3364 x 3364 = 11,318,896.</p>

79 <h3>4.Is 3364 a prime number?</h3>

80 <p>3364 is not a<a>prime number</a>, as it has more than two factors.</p>

81 <h3>5.3364 is divisible by?</h3>

82 <p>3364 has many factors; those are 1, 2, 4, 29, 58, 116, 841, 1682, and 3364.</p>

83 <h2>Important Glossaries for the Square Root of 3364</h2>

84 <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 that is √36 = 6.</li>

85 </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>

86 </ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. Example: 9 is a perfect square because it is 3^2.</li>

87 </ul><ul><li><strong>Prime factorization:</strong>The expression of a number as a product of its prime factors.</li>

88 </ul><ul><li><strong>Long division method:</strong>A method used to find the square root of both perfect and non-perfect squares through step-by-step division.</li>

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

90 <p>▶</p>

91 <h2>Jaskaran Singh Saluja</h2>

92 <h3>About the Author</h3>

93 <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>

94 <h3>Fun Fact</h3>

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