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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 25/9.</p>

4 <h2>What is the Square Root of 25/9?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 25/9 is a<a>perfect square</a><a>fraction</a>. The square root of 25/9 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √(25/9), whereas (25/9)^(1/2) in the exponential form. √(25/9) = 5/3, which is a<a>rational number</a>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 25/9</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, for perfect square fractions like 25/9, we can find the<a>square root</a>by taking the square root of both the<a>numerator</a>and the<a>denominator</a>separately. Let us now learn the following methods: </p>

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

9 <li>Simplification method</li>

10 </ul><h2>Square Root of 25/9 by Prime Factorization Method</h2>

11 <p>The<a>product</a>of prime<a>factors</a>is the Prime factorization of a number. Now let us look at how 25 and 9 are broken down into their prime factors:</p>

12 <p><strong>Step 1:</strong>Finding the prime factors of 25 and 9 - 25 can be broken down as 5 x 5: 5² - 9 can be broken down as 3 x 3: 3²</p>

13 <p><strong>Step 2:</strong>Since both 25 and 9 are perfect squares, we can easily find the square root of each.</p>

14 <p>Thus, √(25/9) = √25/√9 = 5/3.</p>

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17 <h2>Square Root of 25/9 by Simplification Method</h2>

16 <h2>Square Root of 25/9 by Simplification Method</h2>

18 <p>The simplification method involves simplifying the given fraction and then finding the square root.</p>

17 <p>The simplification method involves simplifying the given fraction and then finding the square root.</p>

19 <p><strong>Step 1:</strong>The fraction 25/9 is already in its simplest form.</p>

18 <p><strong>Step 1:</strong>The fraction 25/9 is already in its simplest form.</p>

20 <p><strong>Step 2:</strong>Find the square root of the numerator and the denominator separately: √25 = 5 and √9 = 3.</p>

19 <p><strong>Step 2:</strong>Find the square root of the numerator and the denominator separately: √25 = 5 and √9 = 3.</p>

21 <p><strong>Step 3:</strong>Therefore, √(25/9) = 5/3.</p>

20 <p><strong>Step 3:</strong>Therefore, √(25/9) = 5/3.</p>

22 <h2>Common Mistakes and How to Avoid Them in the Square Root of 25/9</h2>

21 <h2>Common Mistakes and How to Avoid Them in the Square Root of 25/9</h2>

23 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or confusing square roots with cube roots. Now let us look at a few of those mistakes that students tend to make in detail.</p>

22 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or confusing square roots with cube roots. Now let us look at a few of those mistakes that students tend to make in detail.</p>

24 <h3>Problem 1</h3>

23 <h3>Problem 1</h3>

25 <p>Can you help Max find the side length of a square box if its area is given as 25/9 square units?</p>

24 <p>Can you help Max find the side length of a square box if its area is given as 25/9 square units?</p>

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

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

27 <p>The side length of the square is 5/3 units.</p>

26 <p>The side length of the square is 5/3 units.</p>

28 <h3>Explanation</h3>

27 <h3>Explanation</h3>

29 <p>The side length of the square = √(area).</p>

28 <p>The side length of the square = √(area).</p>

30 <p>The area is given as 25/9 square units.</p>

29 <p>The area is given as 25/9 square units.</p>

31 <p>Side length of the square = √(25/9)</p>

30 <p>Side length of the square = √(25/9)</p>

32 <p>= 5/3 units.</p>

31 <p>= 5/3 units.</p>

33 <p>Well explained 👍</p>

32 <p>Well explained 👍</p>

34 <h3>Problem 2</h3>

33 <h3>Problem 2</h3>

35 <p>A rectangular garden has an area of 25/9 square meters. If the width is 1/3 meters, what is the length?</p>

34 <p>A rectangular garden has an area of 25/9 square meters. If the width is 1/3 meters, what is the length?</p>

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

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

37 <p>The length of the garden is 5 meters.</p>

36 <p>The length of the garden is 5 meters.</p>

38 <h3>Explanation</h3>

37 <h3>Explanation</h3>

39 <p>Area of the rectangle = length × width.</p>

38 <p>Area of the rectangle = length × width.</p>

40 <p>Given the area is 25/9 and the width is 1/3 meters.</p>

39 <p>Given the area is 25/9 and the width is 1/3 meters.</p>

41 <p>Length = (Area/Width)</p>

40 <p>Length = (Area/Width)</p>

42 <p>= (25/9) ÷ (1/3)</p>

41 <p>= (25/9) ÷ (1/3)</p>

43 <p>= (25/9) × (3/1)</p>

42 <p>= (25/9) × (3/1)</p>

44 <p>= 25/3</p>

43 <p>= 25/3</p>

45 <p>= 5 meters.</p>

44 <p>= 5 meters.</p>

46 <p>Well explained 👍</p>

45 <p>Well explained 👍</p>

47 <h3>Problem 3</h3>

46 <h3>Problem 3</h3>

48 <p>Calculate √(25/9) × 4.</p>

47 <p>Calculate √(25/9) × 4.</p>

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

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

50 <p>20/3</p>

49 <p>20/3</p>

51 <h3>Explanation</h3>

50 <h3>Explanation</h3>

52 <p>The first step is to find the square root of 25/9, which is 5/3.</p>

51 <p>The first step is to find the square root of 25/9, which is 5/3.</p>

53 <p>The second step is to multiply 5/3 by 4.</p>

52 <p>The second step is to multiply 5/3 by 4.</p>

54 <p>So, (5/3) × 4 = 20/3.</p>

53 <p>So, (5/3) × 4 = 20/3.</p>

55 <p>Well explained 👍</p>

54 <p>Well explained 👍</p>

56 <h3>Problem 4</h3>

55 <h3>Problem 4</h3>

57 <p>What will be the square root of (16 + 9)?</p>

56 <p>What will be the square root of (16 + 9)?</p>

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

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

59 <p>The square root is 5.</p>

58 <p>The square root is 5.</p>

60 <h3>Explanation</h3>

59 <h3>Explanation</h3>

61 <p>To find the square root, we need to find the sum of (16 + 9).</p>

60 <p>To find the square root, we need to find the sum of (16 + 9).</p>

62 <p>16 + 9 = 25, and then √25 = 5.</p>

61 <p>16 + 9 = 25, and then √25 = 5.</p>

63 <p>Therefore, the square root of (16 + 9) is ±5.</p>

62 <p>Therefore, the square root of (16 + 9) is ±5.</p>

64 <p>Well explained 👍</p>

63 <p>Well explained 👍</p>

65 <h3>Problem 5</h3>

64 <h3>Problem 5</h3>

66 <p>Find the perimeter of a rectangle if its length 'l' is √(25/9) units and the width 'w' is 3 units.</p>

65 <p>Find the perimeter of a rectangle if its length 'l' is √(25/9) units and the width 'w' is 3 units.</p>

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

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

68 <p>The perimeter of the rectangle is 16 units.</p>

67 <p>The perimeter of the rectangle is 16 units.</p>

69 <h3>Explanation</h3>

68 <h3>Explanation</h3>

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

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

71 <p>Perimeter = 2 × (√(25/9) + 3)</p>

70 <p>Perimeter = 2 × (√(25/9) + 3)</p>

72 <p>= 2 × (5/3 + 3)</p>

71 <p>= 2 × (5/3 + 3)</p>

73 <p>= 2 × (5/3 + 9/3)</p>

72 <p>= 2 × (5/3 + 9/3)</p>

74 <p>= 2 × 14/3</p>

73 <p>= 2 × 14/3</p>

75 <p>= 28/3</p>

74 <p>= 28/3</p>

76 <p>= 16 units.</p>

75 <p>= 16 units.</p>

77 <p>Well explained 👍</p>

76 <p>Well explained 👍</p>

78 <h2>FAQ on Square Root of 25/9</h2>

77 <h2>FAQ on Square Root of 25/9</h2>

79 <h3>1.What is √(25/9) in its simplest form?</h3>

78 <h3>1.What is √(25/9) in its simplest form?</h3>

80 <p>The simplest form of √(25/9) is achieved by taking the square root of both the numerator and the denominator separately: √25/√9 = 5/3.</p>

79 <p>The simplest form of √(25/9) is achieved by taking the square root of both the numerator and the denominator separately: √25/√9 = 5/3.</p>

81 <h3>2.Mention the factors of 25/9.</h3>

80 <h3>2.Mention the factors of 25/9.</h3>

82 <p>The factors of 25/9 are the factors of 25 and 9 separately.</p>

81 <p>The factors of 25/9 are the factors of 25 and 9 separately.</p>

83 <p>Factors of 25 are 1, 5, and 25.</p>

82 <p>Factors of 25 are 1, 5, and 25.</p>

84 <p>Factors of 9 are 1, 3, and 9.</p>

83 <p>Factors of 9 are 1, 3, and 9.</p>

85 <h3>3.Calculate the square of 25/9.</h3>

84 <h3>3.Calculate the square of 25/9.</h3>

86 <p>We get the square of 25/9 by multiplying the fraction by itself, that is (25/9) × (25/9) = 625/81.</p>

85 <p>We get the square of 25/9 by multiplying the fraction by itself, that is (25/9) × (25/9) = 625/81.</p>

87 <h3>4.Is 25/9 a prime fraction?</h3>

86 <h3>4.Is 25/9 a prime fraction?</h3>

88 <p>25/9 is not a prime fraction, as both the numerator and the denominator have factors other than 1 and themselves.</p>

87 <p>25/9 is not a prime fraction, as both the numerator and the denominator have factors other than 1 and themselves.</p>

89 <h3>5.25/9 is divisible by?</h3>

88 <h3>5.25/9 is divisible by?</h3>

90 <p>25/9 is divisible by the factors of 25 and 9 separately.</p>

89 <p>25/9 is divisible by the factors of 25 and 9 separately.</p>

91 <p>For instance, 25 is divisible by 1, 5, and 25, while 9 is divisible by 1, 3, and 9.</p>

90 <p>For instance, 25 is divisible by 1, 5, and 25, while 9 is divisible by 1, 3, and 9.</p>

92 <h2>Important Glossaries for the Square Root of 25/9</h2>

91 <h2>Important Glossaries for the Square Root of 25/9</h2>

93 <ul><li><strong>Square root:</strong>A square root is the inverse operation to squaring a number. For example, 4² = 16, and the inverse of the square is the square root, √16 = 4. </li>

92 <ul><li><strong>Square root:</strong>A square root is the inverse operation to squaring a number. For example, 4² = 16, and the inverse of the square is the square root, √16 = 4. </li>

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

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

95 <li><strong>Principal square root:</strong>The principal square root is the positive square root of a number. For example, the principal square root of 9 is 3. </li>

94 <li><strong>Principal square root:</strong>The principal square root is the positive square root of a number. For example, the principal square root of 9 is 3. </li>

96 <li><strong>Perfect square:</strong>A perfect square is a number that can be expressed as the square of an integer. For example, 25 is a perfect square because it is 5². </li>

95 <li><strong>Perfect square:</strong>A perfect square is a number that can be expressed as the square of an integer. For example, 25 is a perfect square because it is 5². </li>

97 <li><strong>Fraction:</strong>A fraction is a numerical quantity that is not a whole number, representing a part of a whole. It is expressed as a ratio of two numbers, such as 5/3.</li>

96 <li><strong>Fraction:</strong>A fraction is a numerical quantity that is not a whole number, representing a part of a whole. It is expressed as a ratio of two numbers, such as 5/3.</li>

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

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

99 <p>▶</p>

98 <p>▶</p>

100 <h2>Jaskaran Singh Saluja</h2>

99 <h2>Jaskaran Singh Saluja</h2>

101 <h3>About the Author</h3>

100 <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>

101 <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>

102 <h3>Fun Fact</h3>

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

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