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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as architecture, statistics, and mathematics. Here, we will discuss the square root of 64/25.</p>

4 <h2>What is the Square Root of 64/25?</h2>

5 <p>The<a>square</a>root is the inverse operation<a>of</a>squaring a<a>number</a>. The<a>fraction</a>64/25 is a<a>perfect square</a>because both the<a>numerator and denominator</a>are perfect squares. The square root of 64/25 is expressed in both radical and exponential forms. In radical form, it is expressed as √(64/25), whereas in<a>exponential form</a>it is (64/25)^(1/2). √(64/25) = 8/5, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.</p>

6 <h2>Finding the Square Root of 64/25</h2>

7 <p>The<a>prime factorization</a>method can be used for perfect square numbers. For fractions that are perfect squares, we can directly find the<a>square root</a>of the<a>numerator</a>and the<a>denominator</a>. Let us now learn the following methods:</p>

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

9 <li>Direct square root method</li>

10 </ul><h2>Square Root of 64/25 by Prime Factorization Method</h2>

11 <p>The prime factorization of a number involves expressing it as a<a>product</a>of its prime<a>factors</a>. Let's look at how 64/25 can be expressed:</p>

12 <p><strong>Step 1:</strong>Finding the prime factors of 64 and 25.</p>

13 <p>64 = 2 x 2 x 2 x 2 x 2 x 2 = 2^6</p>

14 <p>25 = 5 x 5 = 5^2</p>

15 <p><strong>Step 2:</strong>Taking the square root of each, we have: √64 = √(2^6) = 2^3 = 8 √25 = √(5^2) = 5</p>

16 <p><strong>Step 3:</strong>Therefore, the square root of 64/25 is 8/5.</p>

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19 <h2>Square Root of 64/25 by Direct Method</h2>

18 <h2>Square Root of 64/25 by Direct Method</h2>

20 <p>The direct method involves finding the square root of both the numerator and the denominator separately:</p>

19 <p>The direct method involves finding the square root of both the numerator and the denominator separately:</p>

21 <p><strong>Step 1:</strong>Find the square root of 64, which is 8, since 8 x 8 = 64.</p>

20 <p><strong>Step 1:</strong>Find the square root of 64, which is 8, since 8 x 8 = 64.</p>

22 <p><strong>Step 2:</strong>Find the square root of 25, which is 5, since 5 x 5 = 25.</p>

21 <p><strong>Step 2:</strong>Find the square root of 25, which is 5, since 5 x 5 = 25.</p>

23 <p><strong>Step 3:</strong>Therefore, the square root of 64/25 is 8/5.</p>

22 <p><strong>Step 3:</strong>Therefore, the square root of 64/25 is 8/5.</p>

24 <h2>Square Root of 64/25 by Approximation Method</h2>

23 <h2>Square Root of 64/25 by Approximation Method</h2>

25 <p>The approximation method generally applies to non-perfect squares, but since 64/25 is a perfect square, we can confirm our result through approximation:</p>

24 <p>The approximation method generally applies to non-perfect squares, but since 64/25 is a perfect square, we can confirm our result through approximation:</p>

26 <p><strong>Step 1:</strong>Recognize that 64/25 is close to 2.56.</p>

25 <p><strong>Step 1:</strong>Recognize that 64/25 is close to 2.56.</p>

27 <p><strong>Step 2:</strong>√(2.56) is approximately 1.6, which is close to 8/5 = 1.6.</p>

26 <p><strong>Step 2:</strong>√(2.56) is approximately 1.6, which is close to 8/5 = 1.6.</p>

28 <h2>Common Mistakes and How to Avoid Them in the Square Root of 64/25</h2>

27 <h2>Common Mistakes and How to Avoid Them in the Square Root of 64/25</h2>

29 <p>Students often make mistakes while finding the square root, such as ignoring the negative square root or not simplifying fractions properly. Let's explore a few common mistakes in detail.</p>

28 <p>Students often make mistakes while finding the square root, such as ignoring the negative square root or not simplifying fractions properly. Let's explore a few common mistakes in detail.</p>

30 <h3>Problem 1</h3>

29 <h3>Problem 1</h3>

31 <p>Can you help Mia find the side length of a square if its area is 64/25 square units?</p>

30 <p>Can you help Mia find the side length of a square if its area is 64/25 square units?</p>

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

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

33 <p>The side length of the square is 8/5 units.</p>

32 <p>The side length of the square is 8/5 units.</p>

34 <h3>Explanation</h3>

33 <h3>Explanation</h3>

35 <p>The side length of a square is the square root of its area.</p>

34 <p>The side length of a square is the square root of its area.</p>

36 <p>Area = 64/25</p>

35 <p>Area = 64/25</p>

37 <p>Side length = √(64/25) = 8/5 units.</p>

36 <p>Side length = √(64/25) = 8/5 units.</p>

38 <p>Well explained 👍</p>

37 <p>Well explained 👍</p>

39 <h3>Problem 2</h3>

38 <h3>Problem 2</h3>

40 <p>A square garden has an area of 64/25 square meters. What is the perimeter?</p>

39 <p>A square garden has an area of 64/25 square meters. What is the perimeter?</p>

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

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

42 <p>The perimeter of the square is 32/5 meters.</p>

41 <p>The perimeter of the square is 32/5 meters.</p>

43 <h3>Explanation</h3>

42 <h3>Explanation</h3>

44 <p>Perimeter of a square = 4 × side length</p>

43 <p>Perimeter of a square = 4 × side length</p>

45 <p>Side length = 8/5 meters</p>

44 <p>Side length = 8/5 meters</p>

46 <p>Perimeter = 4 × 8/5 = 32/5 meters</p>

45 <p>Perimeter = 4 × 8/5 = 32/5 meters</p>

47 <p>Well explained 👍</p>

46 <p>Well explained 👍</p>

48 <h3>Problem 3</h3>

47 <h3>Problem 3</h3>

49 <p>Calculate √(64/25) × 3.</p>

48 <p>Calculate √(64/25) × 3.</p>

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

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

51 <p>The result is 24/5.</p>

50 <p>The result is 24/5.</p>

52 <h3>Explanation</h3>

51 <h3>Explanation</h3>

53 <p>First, find the square root of 64/25, which is 8/5.</p>

52 <p>First, find the square root of 64/25, which is 8/5.</p>

54 <p>Then multiply by 3: (8/5) × 3 = 24/5</p>

53 <p>Then multiply by 3: (8/5) × 3 = 24/5</p>

55 <p>Well explained 👍</p>

54 <p>Well explained 👍</p>

56 <h3>Problem 4</h3>

55 <h3>Problem 4</h3>

57 <p>If a rectangle has a length of √(64/25) and a width of 10/3, what is its area?</p>

56 <p>If a rectangle has a length of √(64/25) and a width of 10/3, what is its area?</p>

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

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

59 <p>The area of the rectangle is 80/15 or simplified to 16/3 square units.</p>

58 <p>The area of the rectangle is 80/15 or simplified to 16/3 square units.</p>

60 <h3>Explanation</h3>

59 <h3>Explanation</h3>

61 <p>Area = length × width Length = 8/5, width = 10/3</p>

60 <p>Area = length × width Length = 8/5, width = 10/3</p>

62 <p>Area = (8/5) × (10/3) = 80/15 = 16/3 square units</p>

61 <p>Area = (8/5) × (10/3) = 80/15 = 16/3 square units</p>

63 <p>Well explained 👍</p>

62 <p>Well explained 👍</p>

64 <h3>Problem 5</h3>

63 <h3>Problem 5</h3>

65 <p>Find the width of a rectangle if its length is 8/5 and perimeter is 34/5.</p>

64 <p>Find the width of a rectangle if its length is 8/5 and perimeter is 34/5.</p>

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

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

67 <p>The width of the rectangle is 9/5 units.</p>

66 <p>The width of the rectangle is 9/5 units.</p>

68 <h3>Explanation</h3>

67 <h3>Explanation</h3>

69 <p>Perimeter of a rectangle = 2 × (length + width) 34/5 = 2 × (8/5 + width) 17/5 = 8/5 + width width = 17/5 - 8/5 = 9/5 units</p>

68 <p>Perimeter of a rectangle = 2 × (length + width) 34/5 = 2 × (8/5 + width) 17/5 = 8/5 + width width = 17/5 - 8/5 = 9/5 units</p>

70 <p>Well explained 👍</p>

69 <p>Well explained 👍</p>

71 <h2>FAQ on Square Root of 64/25</h2>

70 <h2>FAQ on Square Root of 64/25</h2>

72 <h3>1.What is √(64/25) in its simplest form?</h3>

71 <h3>1.What is √(64/25) in its simplest form?</h3>

73 <p>The simplest form of √(64/25) is 8/5.</p>

72 <p>The simplest form of √(64/25) is 8/5.</p>

74 <h3>2.Is 64/25 a perfect square?</h3>

73 <h3>2.Is 64/25 a perfect square?</h3>

75 <p>Yes, 64/25 is a perfect square because both 64 and 25 are perfect squares.</p>

74 <p>Yes, 64/25 is a perfect square because both 64 and 25 are perfect squares.</p>

76 <h3>3.Calculate the square of 64/25.</h3>

75 <h3>3.Calculate the square of 64/25.</h3>

77 <p>The square of 64/25 is 64/25 × 64/25 = 4096/625.</p>

76 <p>The square of 64/25 is 64/25 × 64/25 = 4096/625.</p>

78 <h3>4.Is 64/25 a rational number?</h3>

77 <h3>4.Is 64/25 a rational number?</h3>

79 <h3>5.What is the decimal equivalent of 64/25?</h3>

78 <h3>5.What is the decimal equivalent of 64/25?</h3>

80 <p>The<a>decimal</a>equivalent of 64/25 is 2.56.</p>

79 <p>The<a>decimal</a>equivalent of 64/25 is 2.56.</p>

81 <h2>Important Glossaries for the Square Root of 64/25</h2>

80 <h2>Important Glossaries for the Square Root of 64/25</h2>

82 <ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. For example, the square root of 16 is 4 because 4² = 16.</li>

81 <ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. For example, the square root of 16 is 4 because 4² = 16.</li>

83 </ul><ul><li><strong>Rational number:</strong>A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where the denominator q is not zero.</li>

82 </ul><ul><li><strong>Rational number:</strong>A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where the denominator q is not zero.</li>

84 </ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that has an integer as its square root. For example, 9 is a perfect square because its square root is 3.</li>

83 </ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that has an integer as its square root. For example, 9 is a perfect square because its square root is 3.</li>

85 </ul><ul><li><strong>Fraction:</strong>A fraction consists of a numerator and a denominator, representing a part of a whole. For example, 3/4 is a fraction.</li>

84 </ul><ul><li><strong>Fraction:</strong>A fraction consists of a numerator and a denominator, representing a part of a whole. For example, 3/4 is a fraction.</li>

86 </ul><ul><li><strong>Perimeter:</strong>The perimeter is the total distance around the edge of a two-dimensional shape, such as a rectangle or square.</li>

85 </ul><ul><li><strong>Perimeter:</strong>The perimeter is the total distance around the edge of a two-dimensional shape, such as a rectangle or square.</li>

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

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

88 <p>▶</p>

87 <p>▶</p>

89 <h2>Jaskaran Singh Saluja</h2>

88 <h2>Jaskaran Singh Saluja</h2>

90 <h3>About the Author</h3>

89 <h3>About the Author</h3>

91 <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>

90 <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>

92 <h3>Fun Fact</h3>

91 <h3>Fun Fact</h3>

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

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