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1 - <p>108 Learners</p>

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2 <p>Last updated on<strong>December 15, 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. Square roots are used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 49/25.</p>

4 <h2>What is the Square Root of 49/25?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 49/25 is a<a>perfect square</a><a>fraction</a>.</p>

6 <p>The square root of 49/25 is expressed in both radical and<a>exponential form</a>.</p>

7 <p>In the radical form, it is expressed as √(49/25), whereas (49/25)(1/2) is the exponential form. √(49/25) = 7/5, 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>

8 <h2>Finding the Square Root of 49/25</h2>

9 <p>To find the<a>square root</a>of a perfect square fraction, we take the square root of the<a>numerator</a>and the<a>denominator</a>separately.</p>

10 <p>Let's explore this method:</p>

11 <p>Square root of the numerator: √49 = 7</p>

12 <p>Square root of the denominator: √25 = 5</p>

13 <p>Thus, the square root of 49/25 is 7/5.</p>

14 <h2>Square Root of 49/25 by Prime Factorization Method</h2>

15 <p>The<a>prime factorization</a>method can also be used to find square roots of perfect squares.</p>

16 <p>Let's see how 49/25 can be broken down:</p>

17 <p><strong>Step 1:</strong>Prime factorization of the numerator and the denominator - 49 = 7 x 7 - 25 = 5 x 5</p>

18 <p><strong>Step 2:</strong>Taking the square root of each part - √49 = 7 - √25 = 5</p>

19 <p>Therefore, the square root of 49/25 is 7/5.</p>

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22 <h2>Square Root of 49/25 by Long Division Method</h2>

21 <h2>Square Root of 49/25 by Long Division Method</h2>

23 <p>The<a>long division</a>method is not needed for perfect square fractions like 49/25, as the square roots of the numerator and the denominator can be easily calculated.</p>

22 <p>The<a>long division</a>method is not needed for perfect square fractions like 49/25, as the square roots of the numerator and the denominator can be easily calculated.</p>

24 <p>However, if you wish to use this method, you would start by dividing the<a>numerator and denominator</a>separately and finding their square roots:</p>

23 <p>However, if you wish to use this method, you would start by dividing the<a>numerator and denominator</a>separately and finding their square roots:</p>

25 <p> √49 = 7 using division</p>

24 <p> √49 = 7 using division</p>

26 <p>√25 = 5 using division</p>

25 <p>√25 = 5 using division</p>

27 <p>So, the square root of 49/25 is 7/5.</p>

26 <p>So, the square root of 49/25 is 7/5.</p>

28 <h2>Square Root of 49/25 by Approximation Method</h2>

27 <h2>Square Root of 49/25 by Approximation Method</h2>

29 <p>The approximation method is typically used for non-perfect square numbers.</p>

28 <p>The approximation method is typically used for non-perfect square numbers.</p>

30 <p>For perfect square fractions, direct calculation is more efficient:</p>

29 <p>For perfect square fractions, direct calculation is more efficient:</p>

31 <p><strong>Step 1:</strong>Identify perfect square numbers</p>

30 <p><strong>Step 1:</strong>Identify perfect square numbers</p>

32 <p>√49 = 7,</p>

31 <p>√49 = 7,</p>

33 <p> √25 = 5,</p>

32 <p> √25 = 5,</p>

34 <p>Thus, the square root of 49/25 is directly 7/5.</p>

33 <p>Thus, the square root of 49/25 is directly 7/5.</p>

35 <h2>Common Mistakes and How to Avoid Them in the Square Root of 49/25</h2>

34 <h2>Common Mistakes and How to Avoid Them in the Square Root of 49/25</h2>

36 <p>Students might make mistakes while finding square roots, such as forgetting the properties of fractions or miscalculating individual square roots.</p>

35 <p>Students might make mistakes while finding square roots, such as forgetting the properties of fractions or miscalculating individual square roots.</p>

37 <p>Let us explore some common mistakes in detail.</p>

36 <p>Let us explore some common mistakes in detail.</p>

38 <h3>Problem 1</h3>

37 <h3>Problem 1</h3>

39 <p>Can you help Max find the area of a square box if its side length is given as √(49/25)?</p>

38 <p>Can you help Max find the area of a square box if its side length is given as √(49/25)?</p>

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

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

41 <p>The area of the square is 49/25 square units.</p>

40 <p>The area of the square is 49/25 square units.</p>

42 <h3>Explanation</h3>

41 <h3>Explanation</h3>

43 <p>The area of the square = side2.</p>

42 <p>The area of the square = side2.</p>

44 <p>The side length is given as √(49/25).</p>

43 <p>The side length is given as √(49/25).</p>

45 <p>Area of the square = (√(49/25))2 = (7/5) x (7/5) = 49/25.</p>

44 <p>Area of the square = (√(49/25))2 = (7/5) x (7/5) = 49/25.</p>

46 <p>Therefore, the area of the square box is 49/25 square units.</p>

45 <p>Therefore, the area of the square box is 49/25 square units.</p>

47 <p>Well explained 👍</p>

46 <p>Well explained 👍</p>

48 <h3>Problem 2</h3>

47 <h3>Problem 2</h3>

49 <p>A square field has an area of 49/25 square units. What is the side length of the field?</p>

48 <p>A square field has an area of 49/25 square units. What is the side length of the field?</p>

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

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

51 <p>The side length of the field is 7/5 units.</p>

50 <p>The side length of the field is 7/5 units.</p>

52 <h3>Explanation</h3>

51 <h3>Explanation</h3>

53 <p>If the area of a square is 49/25, then the side length is the square root of 49/25.</p>

52 <p>If the area of a square is 49/25, then the side length is the square root of 49/25.</p>

54 <p>√(49/25) = 7/5.</p>

53 <p>√(49/25) = 7/5.</p>

55 <p>So, the side length of the field is 7/5 units.</p>

54 <p>So, the side length of the field is 7/5 units.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 3</h3>

56 <h3>Problem 3</h3>

58 <p>Calculate 2 x √(49/25).</p>

57 <p>Calculate 2 x √(49/25).</p>

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

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

60 <p>2 x √(49/25) = 14/5</p>

59 <p>2 x √(49/25) = 14/5</p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>First, find the square root of 49/25, which is 7/5.</p>

61 <p>First, find the square root of 49/25, which is 7/5.</p>

63 <p>Then, multiply 7/5 by 2.</p>

62 <p>Then, multiply 7/5 by 2.</p>

64 <p>So, 2 x (7/5) = 14/5.</p>

63 <p>So, 2 x (7/5) = 14/5.</p>

65 <p>Well explained 👍</p>

64 <p>Well explained 👍</p>

66 <h3>Problem 4</h3>

65 <h3>Problem 4</h3>

67 <p>What is the square root of (49/25) x 25?</p>

66 <p>What is the square root of (49/25) x 25?</p>

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

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

69 <p>The square root is 7.</p>

68 <p>The square root is 7.</p>

70 <h3>Explanation</h3>

69 <h3>Explanation</h3>

71 <p>First, simplify (49/25) x 25 = 49.</p>

70 <p>First, simplify (49/25) x 25 = 49.</p>

72 <p>Then, the square root of 49 is 7.</p>

71 <p>Then, the square root of 49 is 7.</p>

73 <p>Therefore, the square root is ±7.</p>

72 <p>Therefore, the square root is ±7.</p>

74 <p>Well explained 👍</p>

73 <p>Well explained 👍</p>

75 <h3>Problem 5</h3>

74 <h3>Problem 5</h3>

76 <p>Find the perimeter of a rectangle if its length 'l' is √(49/25) units and the width 'w' is 10 units.</p>

75 <p>Find the perimeter of a rectangle if its length 'l' is √(49/25) units and the width 'w' is 10 units.</p>

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

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

78 <p>The perimeter of the rectangle is 24 units.</p>

77 <p>The perimeter of the rectangle is 24 units.</p>

79 <h3>Explanation</h3>

78 <h3>Explanation</h3>

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

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

81 <p>Perimeter = 2 × (√(49/25) + 10)</p>

80 <p>Perimeter = 2 × (√(49/25) + 10)</p>

82 <p>= 2 × (7/5 + 10).</p>

81 <p>= 2 × (7/5 + 10).</p>

83 <p>Convert 10 to a fraction:</p>

82 <p>Convert 10 to a fraction:</p>

84 <p>10 = 50/5.</p>

83 <p>10 = 50/5.</p>

85 <p>So, Perimeter = 2 × (7/5 + 50/5)</p>

84 <p>So, Perimeter = 2 × (7/5 + 50/5)</p>

86 <p>= 2 × (57/5)</p>

85 <p>= 2 × (57/5)</p>

87 <p>= 114/5</p>

86 <p>= 114/5</p>

88 <p>= 22.8 units.</p>

87 <p>= 22.8 units.</p>

89 <p>Well explained 👍</p>

88 <p>Well explained 👍</p>

90 <h2>FAQ on Square Root of 49/25</h2>

89 <h2>FAQ on Square Root of 49/25</h2>

91 <h3>1.What is √(49/25) in its simplest form?</h3>

90 <h3>1.What is √(49/25) in its simplest form?</h3>

92 <p>The simplest form of √(49/25) is 7/5, as both the numerator (49) and the denominator (25) are perfect squares.</p>

91 <p>The simplest form of √(49/25) is 7/5, as both the numerator (49) and the denominator (25) are perfect squares.</p>

93 <h3>2.How do you find the square root of a fraction?</h3>

92 <h3>2.How do you find the square root of a fraction?</h3>

94 <p>To find the square root of a fraction, find the square root of the numerator and the square root of the denominator separately. Then, divide the two results.</p>

93 <p>To find the square root of a fraction, find the square root of the numerator and the square root of the denominator separately. Then, divide the two results.</p>

95 <h3>3.Is 49/25 a rational number?</h3>

94 <h3>3.Is 49/25 a rational number?</h3>

96 <p>Yes, 49/25 is a rational number because it can be expressed as a fraction where both the numerator and the denominator are integers.</p>

95 <p>Yes, 49/25 is a rational number because it can be expressed as a fraction where both the numerator and the denominator are integers.</p>

97 <h3>4.What is the decimal form of √(49/25)?</h3>

96 <h3>4.What is the decimal form of √(49/25)?</h3>

98 <p>The<a>decimal</a>form of √(49/25) is 1.4, as 7 divided by 5 equals 1.4.</p>

97 <p>The<a>decimal</a>form of √(49/25) is 1.4, as 7 divided by 5 equals 1.4.</p>

99 <h3>5.Is √(49/25) greater than 1?</h3>

98 <h3>5.Is √(49/25) greater than 1?</h3>

100 <p>Yes, √(49/25) is<a>greater than</a>1 because 7/5 is equal to 1.4, which is greater than 1.</p>

99 <p>Yes, √(49/25) is<a>greater than</a>1 because 7/5 is equal to 1.4, which is greater than 1.</p>

101 <h2>Important Glossaries for the Square Root of 49/25</h2>

100 <h2>Important Glossaries for the Square Root of 49/25</h2>

102 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, if 42 = 16, then the square root of 16 is √16 = 4.</li>

101 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, if 42 = 16, then the square root of 16 is √16 = 4.</li>

103 <li><strong>Rational number:</strong>A rational number can be expressed as a fraction p/q, where p and q are integers, and q is not zero.</li>

102 <li><strong>Rational number:</strong>A rational number can be expressed as a fraction p/q, where p and q are integers, and q is not zero.</li>

104 <li><strong>Perfect square:</strong>A number is a perfect square if it can be expressed as the square of an integer. For example, 49 is a perfect square because it is 72.</li>

103 <li><strong>Perfect square:</strong>A number is a perfect square if it can be expressed as the square of an integer. For example, 49 is a perfect square because it is 72.</li>

105 <li><strong>Fraction:</strong>A fraction represents a part of a whole and is expressed as a ratio of two numbers, the numerator and the denominator.</li>

104 <li><strong>Fraction:</strong>A fraction represents a part of a whole and is expressed as a ratio of two numbers, the numerator and the denominator.</li>

106 <li><strong>Decimal:</strong>A decimal is a number that consists of a whole number and a fractional part separated by a decimal point, such as 1.4.</li>

105 <li><strong>Decimal:</strong>A decimal is a number that consists of a whole number and a fractional part separated by a decimal point, such as 1.4.</li>

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

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

108 <p>▶</p>

107 <p>▶</p>

109 <h2>Jaskaran Singh Saluja</h2>

108 <h2>Jaskaran Singh Saluja</h2>

110 <h3>About the Author</h3>

109 <h3>About the Author</h3>

111 <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>

110 <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>

112 <h3>Fun Fact</h3>

111 <h3>Fun Fact</h3>

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

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