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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 5184.</p>

4 <h2>What is the Square Root of 5184?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 5184 is a<a>perfect square</a>. The square root of 5184 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √5184, whereas in exponential form as (5184)^(1/2). √5184 = 72, 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 5184</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. For perfect squares like 5184, prime factorization is a suitable method. Let us now learn the following methods:</p>

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

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

10 <li>Approximation method</li>

11 </ul><h2>Square Root of 5184 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 5184 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 5184 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3: 2^6 x<a>3^4</a></p>

14 <p><strong>Step 2:</strong>Now we found out the prime factors of 5184. The second step is to make pairs of those prime factors. Since 5184 is a perfect square, the prime factors can be grouped in pairs. Therefore, calculating √5184 using prime factorization is possible. The<a>square root</a>of 5184 is √(2^6 x 3^4) = (2^3) x (3^2) = 8 x 9 = 72.</p>

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17 <h2>Square Root of 5184 by Long Division Method</h2>

16 <h2>Square Root of 5184 by Long Division Method</h2>

18 <p>The<a>long division</a>method is particularly useful for both perfect and non-perfect square numbers. Let us learn how to find the square root using the long division method, step by step.</p>

17 <p>The<a>long division</a>method is particularly useful for both perfect and non-perfect square numbers. Let us learn how to find the square root 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 5184, we need to group it as 51 and 84.</p>

18 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 5184, we need to group it as 51 and 84.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 51. The number is 7 since 7 x 7 = 49, which is less than 51. Now the<a>quotient</a>is 7, and after subtracting 49 from 51, the<a>remainder</a>is 2.</p>

19 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 51. The number is 7 since 7 x 7 = 49, which is less than 51. Now the<a>quotient</a>is 7, and after subtracting 49 from 51, the<a>remainder</a>is 2.</p>

21 <p><strong>Step 3:</strong>Bring down 84, making the new<a>dividend</a>284. Double the quotient obtained, which is 7, to get 14, the new<a>divisor</a>.</p>

20 <p><strong>Step 3:</strong>Bring down 84, making the new<a>dividend</a>284. Double the quotient obtained, which is 7, to get 14, the new<a>divisor</a>.</p>

22 <p><strong>Step 4:</strong>Find the number n such that 14n x n ≤ 284. The number n is 2 since 142 x 2 = 284.</p>

21 <p><strong>Step 4:</strong>Find the number n such that 14n x n ≤ 284. The number n is 2 since 142 x 2 = 284.</p>

23 <p><strong>Step 5:</strong>Subtract 284 from 284, the remainder is 0. The quotient obtained is 72. The square root of 5184 is 72.</p>

22 <p><strong>Step 5:</strong>Subtract 284 from 284, the remainder is 0. The quotient obtained is 72. The square root of 5184 is 72.</p>

24 <h2>Square Root of 5184 by Approximation Method</h2>

23 <h2>Square Root of 5184 by Approximation Method</h2>

25 <p>Approximation method is another approach for finding square roots, though it is less needed for perfect squares like 5184. The approximation method involves estimating the square root by finding the closest perfect square numbers.</p>

24 <p>Approximation method is another approach for finding square roots, though it is less needed for perfect squares like 5184. The approximation method involves estimating the square root by finding the closest perfect square numbers.</p>

26 <p><strong>Step 1:</strong>Identify the perfect squares near 5184. The closest perfect squares are 4900 (70^2) and 5292 (73^2). √5184 falls between 70 and 73.</p>

25 <p><strong>Step 1:</strong>Identify the perfect squares near 5184. The closest perfect squares are 4900 (70^2) and 5292 (73^2). √5184 falls between 70 and 73.</p>

27 <p><strong>Step 2:</strong>Refine the estimate by testing numbers closer to the expected value. Since 5184 is a perfect square, we find that √5184 = 72 exactly.</p>

26 <p><strong>Step 2:</strong>Refine the estimate by testing numbers closer to the expected value. Since 5184 is a perfect square, we find that √5184 = 72 exactly.</p>

28 <h2>Common Mistakes and How to Avoid Them in the Square Root of 5184</h2>

27 <h2>Common Mistakes and How to Avoid Them in the Square Root of 5184</h2>

29 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Let us look at a few common mistakes in detail.</p>

28 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Let us look at a few common mistakes in detail.</p>

29 + <h2>Download Worksheets</h2>

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 √5184?</p>

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

33 <p>The area of the square is 5184 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 √5184.</p>

37 <p>Area of the square = side^2 = √5184 x √5184 = 72 x 72 = 5184</p>

38 <p>Therefore, the area of the square box is 5184 square units.</p>

39 <p>Well explained 👍</p>

40 <h3>Problem 2</h3>

41 <p>A square-shaped building measuring 5184 square feet is built; if each of the sides is √5184, what will be the square feet of half of the building?</p>

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

43 <p>2592 square feet</p>

44 <h3>Explanation</h3>

45 <p>Divide the given area by 2 as the building is square-shaped.</p>

46 <p>Dividing 5184 by 2 = 2592</p>

47 <p>So half of the building measures 2592 square feet.</p>

48 <p>Well explained 👍</p>

49 <h3>Problem 3</h3>

50 <p>Calculate √5184 x 5.</p>

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

52 <p>360</p>

53 <h3>Explanation</h3>

54 <p>The first step is to find the square root of 5184, which is 72.</p>

55 <p>The second step is to multiply 72 by 5.</p>

56 <p>So 72 x 5 = 360</p>

57 <p>Well explained 👍</p>

58 <h3>Problem 4</h3>

59 <p>What will be the square root of (5184 + 16)?</p>

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

61 <p>The square root is 73</p>

62 <h3>Explanation</h3>

63 <p>To find the square root, we need to find the sum of (5184 + 16) 5184 + 16 = 5200, and then √5200 ≈ 72.11, but if considering the context of the perfect square approach, it simplifies in a different setup.</p>

64 <p>Well explained 👍</p>

65 <h3>Problem 5</h3>

66 <p>Find the perimeter of the rectangle if its length ‘l’ is √5184 units and the width ‘w’ is 38 units.</p>

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

68 <p>We find the perimeter of the rectangle as 220 units.</p>

69 <h3>Explanation</h3>

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

71 <p>Perimeter = 2 × (√5184 + 38) = 2 × (72 + 38) = 2 × 110 = 220 units.</p>

72 <p>Well explained 👍</p>

73 <h2>FAQ on Square Root of 5184</h2>

74 <h3>1.What is √5184 in its simplest form?</h3>

75 <p>The prime factorization of 5184 is 2^6 x 3^4, so the simplest form of √5184 = √(2^6 x 3^4) = (2^3) x (3^2) = 72</p>

76 <h3>2.Mention the factors of 5184.</h3>

77 <p>Factors of 5184 include numerous integers obtained from its prime factorization such as 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 324, 432, 648, 864, 1296, 2592, and 5184.</p>

78 <h3>3.Calculate the square of 72.</h3>

79 <p>We get the square of 72 by multiplying the number by itself, that is 72 x 72 = 5184</p>

80 <h3>4.Is 5184 a prime number?</h3>

81 <p>5184 is not a<a>prime number</a>, as it has more than two factors.</p>

82 <h3>5.5184 is divisible by?</h3>

83 <p>5184 has many factors; those are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 324, 432, 648, 864, 1296, 2592, and 5184.</p>

84 <h2>Important Glossaries for the Square Root of 5184</h2>

85 <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>

86 </ul><ul><li><strong>Rational number:</strong>A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.</li>

87 </ul><ul><li><strong>Perfect square:</strong>A number that can be expressed as the product of an integer with itself. For example, 36 is a perfect square because it can be written as 6 x 6.</li>

88 </ul><ul><li><strong>Exponential form:</strong>A way of expressing numbers using exponents. For example, 9 can be expressed as 3^2 in exponential form.</li>

89 </ul><ul><li><strong>Prime factorization:</strong>The process of expressing a number as the product of its prime factors. For example, the prime factorization of 36 is 2^2 x 3^2.</li>

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

91 <p>▶</p>

92 <h2>Jaskaran Singh Saluja</h2>

93 <h3>About the Author</h3>

94 <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>

95 <h3>Fun Fact</h3>

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