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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. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 49/144.</p>

4 <h2>What is the Square Root of 49/144?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>.</p>

6 <p>The<a>fraction</a>49/144 is a<a>perfect square</a>, as both the<a>numerator and denominator</a>are perfect squares.</p>

7 <p>The square root of 49/144 is expressed in both radical and<a>exponential form</a>.</p>

8 <p>In the radical form, it is expressed as √(49/144), whereas (49/144)(1/2) in exponential form. √(49/144) = 7/12, 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>

9 <h2>Finding the Square Root of 49/144</h2>

10 <p>The<a>prime factorization</a>method can be used for perfect square numbers.</p>

11 <p>For fractions that are perfect squares, we can find the<a>square root</a>of both the<a>numerator</a>and the<a>denominator</a>separately.</p>

12 <p>Let us now learn the following methods:</p>

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

14 <li>Simplification method</li>

15 </ul><h2>Square Root of 49/144 by Prime Factorization Method</h2>

16 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number.</p>

17 <p>Now, let us look at how 49 and 144 are broken down into their prime factors:</p>

18 <p><strong>Step 1:</strong>Finding the prime factors of 49 and 144. - 49 = 7 x 7 = 7² - 144 = 2 x 2 x 2 x 2 x 3 x 3 = 2⁴ x 3²</p>

19 <p><strong>Step 2:</strong>Since both 49 and 144 are perfect squares, we can directly find the square roots: - √49 = 7 - √144 = 12</p>

20 <p>Therefore, √(49/144) = 7/12.</p>

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23 <h2>Square Root of 49/144 by Simplification Method</h2>

22 <h2>Square Root of 49/144 by Simplification Method</h2>

24 <p>The simplification method is a straightforward approach to finding the square roots of fractions.</p>

23 <p>The simplification method is a straightforward approach to finding the square roots of fractions.</p>

25 <p>Let us learn how to find the square root of 49/144 using simplification:</p>

24 <p>Let us learn how to find the square root of 49/144 using simplification:</p>

26 <p><strong>Step 1:</strong>Identify the perfect squares in the numerator and the denominator. - √49 = 7 - √144 = 12</p>

25 <p><strong>Step 1:</strong>Identify the perfect squares in the numerator and the denominator. - √49 = 7 - √144 = 12</p>

27 <p><strong>Step 2:</strong>Simplify the square root of the fraction by taking the square root of the numerator and the denominator separately: - √(49/144) = 7/12</p>

26 <p><strong>Step 2:</strong>Simplify the square root of the fraction by taking the square root of the numerator and the denominator separately: - √(49/144) = 7/12</p>

28 <p>Thus, the square root of 49/144 is 7/12.</p>

27 <p>Thus, the square root of 49/144 is 7/12.</p>

29 <h2>Common Mistakes and How to Avoid Them in the Square Root of 49/144</h2>

28 <h2>Common Mistakes and How to Avoid Them in the Square Root of 49/144</h2>

30 <p>Students often make mistakes while finding the square root of fractions, such as not simplifying the fraction first or incorrectly applying the square root separately to the numerator and denominator.</p>

29 <p>Students often make mistakes while finding the square root of fractions, such as not simplifying the fraction first or incorrectly applying the square root separately to the numerator and denominator.</p>

31 <p>Let us look at a few common mistakes and how to avoid them.</p>

30 <p>Let us look at a few common mistakes and how to avoid them.</p>

32 <h3>Problem 1</h3>

31 <h3>Problem 1</h3>

33 <p>Can you help Max find the side length of a square if its area is 49/144 square units?</p>

32 <p>Can you help Max find the side length of a square if its area is 49/144 square units?</p>

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

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

35 <p>The side length of the square is 7/12 units.</p>

34 <p>The side length of the square is 7/12 units.</p>

36 <h3>Explanation</h3>

35 <h3>Explanation</h3>

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

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

38 <p>The area is given as 49/144 square units.</p>

37 <p>The area is given as 49/144 square units.</p>

39 <p>Therefore, side = √(49/144) = 7/12.</p>

38 <p>Therefore, side = √(49/144) = 7/12.</p>

40 <p>Thus, the side length of the square is 7/12 units.</p>

39 <p>Thus, the side length of the square is 7/12 units.</p>

41 <p>Well explained 👍</p>

40 <p>Well explained 👍</p>

42 <h3>Problem 2</h3>

41 <h3>Problem 2</h3>

43 <p>A rectangular garden has an area of 49/144 square meters. If the length is √49 meters, what is the width of the garden?</p>

42 <p>A rectangular garden has an area of 49/144 square meters. If the length is √49 meters, what is the width of the garden?</p>

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

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

45 <p>The width of the garden is 1/12 meters.</p>

44 <p>The width of the garden is 1/12 meters.</p>

46 <h3>Explanation</h3>

45 <h3>Explanation</h3>

47 <p>The area of the rectangle = length × width.</p>

46 <p>The area of the rectangle = length × width.</p>

48 <p>Given, length = √49 = 7 meters and</p>

47 <p>Given, length = √49 = 7 meters and</p>

49 <p>area = 49/144 square meters.</p>

48 <p>area = 49/144 square meters.</p>

50 <p>Width = Area / Length</p>

49 <p>Width = Area / Length</p>

51 <p>= (49/144) / 7</p>

50 <p>= (49/144) / 7</p>

52 <p>= 1/12 meters.</p>

51 <p>= 1/12 meters.</p>

53 <p>Well explained 👍</p>

52 <p>Well explained 👍</p>

54 <h3>Problem 3</h3>

53 <h3>Problem 3</h3>

55 <p>Calculate 5 × √(49/144).</p>

54 <p>Calculate 5 × √(49/144).</p>

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

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

57 <p>The result is 35/12.</p>

56 <p>The result is 35/12.</p>

58 <h3>Explanation</h3>

57 <h3>Explanation</h3>

59 <p>First, find the square root of 49/144, which is 7/12.</p>

58 <p>First, find the square root of 49/144, which is 7/12.</p>

60 <p>Then, multiply by 5:</p>

59 <p>Then, multiply by 5:</p>

61 <p>5 × 7/12 = 35/12.</p>

60 <p>5 × 7/12 = 35/12.</p>

62 <p>Well explained 👍</p>

61 <p>Well explained 👍</p>

63 <h3>Problem 4</h3>

62 <h3>Problem 4</h3>

64 <p>What is the square root of (49 + 95/144)?</p>

63 <p>What is the square root of (49 + 95/144)?</p>

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

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

66 <p>The square root is 13/12.</p>

65 <p>The square root is 13/12.</p>

67 <h3>Explanation</h3>

66 <h3>Explanation</h3>

68 <p>First, find the sum: 49 + 95/144</p>

67 <p>First, find the sum: 49 + 95/144</p>

69 <p>= 49/1 + 95/144</p>

68 <p>= 49/1 + 95/144</p>

70 <p>= 7201/144.</p>

69 <p>= 7201/144.</p>

71 <p>Then, find the square root:</p>

70 <p>Then, find the square root:</p>

72 <p>√(7201/144) = 13/12.</p>

71 <p>√(7201/144) = 13/12.</p>

73 <p>Well explained 👍</p>

72 <p>Well explained 👍</p>

74 <h3>Problem 5</h3>

73 <h3>Problem 5</h3>

75 <p>A square plot measures 49/144 square meters in area. What is the perimeter of the plot?</p>

74 <p>A square plot measures 49/144 square meters in area. What is the perimeter of the plot?</p>

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

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

77 <p>The perimeter of the plot is 28/12 meters, or 7/3 meters.</p>

76 <p>The perimeter of the plot is 28/12 meters, or 7/3 meters.</p>

78 <h3>Explanation</h3>

77 <h3>Explanation</h3>

79 <p>Side of the square = √(49/144) = 7/12.</p>

78 <p>Side of the square = √(49/144) = 7/12.</p>

80 <p>Perimeter of the square = 4 × side</p>

79 <p>Perimeter of the square = 4 × side</p>

81 <p>= 4 × 7/12</p>

80 <p>= 4 × 7/12</p>

82 <p>= 28/12 meters or 7/3 meters.</p>

81 <p>= 28/12 meters or 7/3 meters.</p>

83 <p>Well explained 👍</p>

82 <p>Well explained 👍</p>

84 <h2>FAQ on Square Root of 49/144</h2>

83 <h2>FAQ on Square Root of 49/144</h2>

85 <h3>1.What is √(49/144) in its simplest form?</h3>

84 <h3>1.What is √(49/144) in its simplest form?</h3>

86 <p>The simplest form of √(49/144) is 7/12.</p>

85 <p>The simplest form of √(49/144) is 7/12.</p>

87 <h3>2.Mention the factors of 49 and 144.</h3>

86 <h3>2.Mention the factors of 49 and 144.</h3>

88 <p>Factors of 49 are 1, 7, and 49. Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.</p>

87 <p>Factors of 49 are 1, 7, and 49. Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.</p>

89 <h3>3.Calculate the square of 49/144.</h3>

88 <h3>3.Calculate the square of 49/144.</h3>

90 <p>The square of 49/144 is (49/144)² = 2401/20736.</p>

89 <p>The square of 49/144 is (49/144)² = 2401/20736.</p>

91 <h3>4.Is 49/144 a rational number?</h3>

90 <h3>4.Is 49/144 a rational number?</h3>

92 <p>Yes, 49/144 is a rational number because it can be expressed as a<a>ratio</a>of two<a>integers</a>.</p>

91 <p>Yes, 49/144 is a rational number because it can be expressed as a<a>ratio</a>of two<a>integers</a>.</p>

93 <h3>5.Is (49/144) a perfect square?</h3>

92 <h3>5.Is (49/144) a perfect square?</h3>

94 <p>Yes, 49/144 is a perfect square because both the numerator and denominator are perfect squares.</p>

93 <p>Yes, 49/144 is a perfect square because both the numerator and denominator are perfect squares.</p>

95 <h2>Important Glossaries for the Square Root of 49/144</h2>

94 <h2>Important Glossaries for the Square Root of 49/144</h2>

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

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

97 <li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 49 and 144 are perfect squares.</li>

96 <li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 49 and 144 are perfect squares.</li>

98 <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 q is not zero.</li>

97 <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 q is not zero.</li>

99 <li><strong>Fraction:</strong>A fraction represents a part of a whole or any number of equal parts. It is expressed as p/q, where p and q are integers, and q ≠ 0.</li>

98 <li><strong>Fraction:</strong>A fraction represents a part of a whole or any number of equal parts. It is expressed as p/q, where p and q are integers, and q ≠ 0.</li>

100 <li><strong>Simplification:</strong>The process of reducing a mathematical expression to its simplest form. In fractions, it involves finding and dividing by the greatest common divisor of the numerator and denominator.</li>

99 <li><strong>Simplification:</strong>The process of reducing a mathematical expression to its simplest form. In fractions, it involves finding and dividing by the greatest common divisor of the numerator and denominator.</li>

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

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

102 <p>▶</p>

101 <p>▶</p>

103 <h2>Jaskaran Singh Saluja</h2>

102 <h2>Jaskaran Singh Saluja</h2>

104 <h3>About the Author</h3>

103 <h3>About the Author</h3>

105 <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>

104 <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>

106 <h3>Fun Fact</h3>

105 <h3>Fun Fact</h3>

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

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