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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 like vehicle design, finance, etc. Here, we will discuss the square root of 8464.</p>

4 <h2>What is the Square Root of 8464?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 8464 is a<a>perfect square</a>. The square root of 8464 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √8464, whereas (8464)^(1/2) in the exponential form. √8464 = 92, 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 8464</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. The<a>long division</a>method and approximation method can also be used to find square roots. 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 8464 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 8464 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 8464 Breaking it down, we get 2 x 2 x 2 x 2 x 13 x 13: 2^4 x 13^2</p>

14 <p><strong>Step 2:</strong>Now we found out the prime factors of 8464. The next step is to make pairs of those prime factors. Since 8464 is a perfect square, we can group the digits into pairs. Therefore, calculating 8464 using prime factorization is possible.</p>

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17 <h2>Square Root of 8464 by Long Division Method</h2>

16 <h2>Square Root of 8464 by Long Division Method</h2>

18 <p>The long<a>division</a>method is particularly useful for non-perfect square numbers, but it can also confirm results for perfect squares. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>

17 <p>The long<a>division</a>method is particularly useful for non-perfect square numbers, but it can also confirm results for perfect squares. 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 8464, we group it as 84 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 8464, we group it as 84 and 64.</p>

20 <p><strong>Step 2:</strong>Find a number whose square is<a>less than</a>or equal to 84. This is 9 because 9 x 9 = 81.</p>

19 <p><strong>Step 2:</strong>Find a number whose square is<a>less than</a>or equal to 84. This is 9 because 9 x 9 = 81.</p>

21 <p><strong>Step 3:</strong>The<a>quotient</a>is 9. Subtract 81 from 84, the<a>remainder</a>is 3. Bring down the next pair, 64, to make the new<a>dividend</a>364.</p>

20 <p><strong>Step 3:</strong>The<a>quotient</a>is 9. Subtract 81 from 84, the<a>remainder</a>is 3. Bring down the next pair, 64, to make the new<a>dividend</a>364.</p>

22 <p><strong>Step 4:</strong>Double the quotient and use it as part of the new<a>divisor</a>. So, 9 x 2 = 18.</p>

21 <p><strong>Step 4:</strong>Double the quotient and use it as part of the new<a>divisor</a>. So, 9 x 2 = 18.</p>

23 <p><strong>Step 5:</strong>Find a digit n such that 18n x n is less than or equal to 364. Here, n is 2, because 182 x 2 = 364.</p>

22 <p><strong>Step 5:</strong>Find a digit n such that 18n x n is less than or equal to 364. Here, n is 2, because 182 x 2 = 364.</p>

24 <p><strong>Step 6:</strong>Subtract 364 from 364 to get a remainder of 0. Since there's no remainder, the quotient is 92, confirming √8464 = 92.</p>

23 <p><strong>Step 6:</strong>Subtract 364 from 364 to get a remainder of 0. Since there's no remainder, the quotient is 92, confirming √8464 = 92.</p>

25 <h2>Square Root of 8464 by Approximation Method</h2>

24 <h2>Square Root of 8464 by Approximation Method</h2>

26 <p>The approximation method is an easy method for finding the square roots of non-perfect squares but can confirm perfect squares by showing proximity to calculated roots.</p>

25 <p>The approximation method is an easy method for finding the square roots of non-perfect squares but can confirm perfect squares by showing proximity to calculated roots.</p>

27 <p><strong>Step 1:</strong>Find the closest perfect square numbers around 8464. Since 8464 is a perfect square, its square root is exactly between 91 and 93.</p>

26 <p><strong>Step 1:</strong>Find the closest perfect square numbers around 8464. Since 8464 is a perfect square, its square root is exactly between 91 and 93.</p>

28 <p><strong>Step 2:</strong>Verify by calculating: 91^2 = 8281 and 93^2 = 8649. Since 8464 is exactly between these, it confirms √8464 = 92.</p>

27 <p><strong>Step 2:</strong>Verify by calculating: 91^2 = 8281 and 93^2 = 8649. Since 8464 is exactly between these, it confirms √8464 = 92.</p>

29 <h2>Common Mistakes and How to Avoid Them in the Square Root of 8464</h2>

28 <h2>Common Mistakes and How to Avoid Them in the Square Root of 8464</h2>

30 <p>Students can make mistakes while finding the square root, such as forgetting about the negative square root, or skipping steps in methods. Let us look at a few of these mistakes in detail.</p>

29 <p>Students can make mistakes while finding the square root, such as forgetting about the negative square root, or skipping steps in methods. Let us look at a few of these mistakes in detail.</p>

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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 √8464?</p>

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

34 <p>The area of the square is 8464 square units.</p>

35 <h3>Explanation</h3>

36 <p>The area of the square = side^2. The side length is given as √8464. Area of the square = side^2 = √8464 x √8464 = 92 x 92 = 8464. Therefore, the area of the square box is 8464 square units.</p>

37 <p>Well explained 👍</p>

38 <h3>Problem 2</h3>

39 <p>A square-shaped building measuring 8464 square feet is built; if each of the sides is √8464, what will be the square feet of half of the building?</p>

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

41 <p>4232 square feet</p>

42 <h3>Explanation</h3>

43 <p>We can divide the given area by 2 as the building is square-shaped. Dividing 8464 by 2 = we get 4232. So half of the building measures 4232 square feet.</p>

44 <p>Well explained 👍</p>

45 <h3>Problem 3</h3>

46 <p>Calculate √8464 x 5.</p>

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

48 <p>460</p>

49 <h3>Explanation</h3>

50 <p>The first step is to find the square root of 8464, which is 92. The second step is to multiply 92 by 5. So 92 x 5 = 460.</p>

51 <p>Well explained 👍</p>

52 <h3>Problem 4</h3>

53 <p>What will be the square root of (8464 + 36)?</p>

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

55 <p>The square root is 97</p>

56 <h3>Explanation</h3>

57 <p>To find the square root, we need to find the sum of (8464 + 36). 8464 + 36 = 8500, and the approximate square root of 8500 is 97.07, rounded to 97. Therefore, the square root of (8464 + 36) is approximately ±97.</p>

58 <p>Well explained 👍</p>

59 <h3>Problem 5</h3>

60 <p>Find the perimeter of the rectangle if its length ‘l’ is √8464 units and the width ‘w’ is 38 units.</p>

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

62 <p>The perimeter of the rectangle is 260 units.</p>

63 <h3>Explanation</h3>

64 <p>Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√8464 + 38) = 2 × (92 + 38) = 2 × 130 = 260 units.</p>

65 <p>Well explained 👍</p>

66 <h2>FAQ on Square Root of 8464</h2>

67 <h3>1.What is √8464 in its simplest form?</h3>

68 <p>The prime factorization of 8464 is 2 x 2 x 2 x 2 x 13 x 13, so the simplest form of √8464 = √(2^4 x 13^2) = 92.</p>

69 <h3>2.Mention the factors of 8464.</h3>

70 <p>Factors of 8464 include 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 1690, 3380, 8464.</p>

71 <h3>3.Calculate the square of 8464.</h3>

72 <p>We get the square of 8464 by multiplying the number by itself, that is 8464 x 8464.</p>

73 <h3>4.Is 8464 a prime number?</h3>

74 <p>8464 is not a<a>prime number</a>, as it has more than two factors.</p>

75 <h3>5.8464 is divisible by?</h3>

76 <p>8464 has many factors; those are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 1690, 3380, and 8464.</p>

77 <h2>Important Glossaries for the Square Root of 8464</h2>

78 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 9^2 = 81, and the inverse of the square is the square root, that is √81 = 9. </li>

79 <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>

80 <li><strong>Perfect square:</strong>A number that is the square of an integer. For example, 64 is a perfect square because it is 8^2. </li>

81 <li><strong>Prime factorization:</strong>The process of expressing a number as a product of its prime factors. For example, the prime factorization of 8464 is 2^4 x 13^2. </li>

82 <li><strong>Long division method:</strong>A method used to find the square root of a number by dividing and averaging. This is particularly useful for non-perfect squares but can confirm perfect squares.</li>

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

84 <p>▶</p>

85 <h2>Jaskaran Singh Saluja</h2>

86 <h3>About the Author</h3>

87 <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>

88 <h3>Fun Fact</h3>

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