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1 - <p>112 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. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 6/5.</p>

4 <h2>What is the Square Root of 6/5?</h2>

5 <p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 6/5 is not a<a>perfect square</a>.</p>

6 <p>The square root of 6/5 is expressed in both radical and exponential forms.</p>

7 <p>In the radical form, it is expressed as √(6/5), whereas (6/5)(1/2) in the<a>exponential form</a>.</p>

8 <p>√(6/5) = 1.09545, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>

9 <h2>Finding the Square Root of 6/5</h2>

10 <p>The<a>prime factorization</a>method is useful for perfect square numbers.</p>

11 <p>However, for non-perfect square numbers, methods like long-<a>division</a>and approximation are used.</p>

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

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

14 <li>Long division method </li>

15 <li>Approximation method</li>

16 </ul><h2>Square Root of 6/5 by Prime Factorization Method</h2>

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

18 <p>Since 6/5 is a<a>fraction</a>, we perform the prime factorization of both the<a>numerator</a>and the<a>denominator</a>.</p>

19 <p><strong>Step 1:</strong>Finding the prime factors of 6 and 5 6 can be broken down into 2 x 3, and 5 is already a<a>prime number</a>.</p>

20 <p><strong>Step 2:</strong>Since 6/5 is not a perfect square, the prime factorization method cannot be directly used to find its<a>square root</a>.</p>

21 <p>Therefore, using prime factorization for 6/5 is not possible.</p>

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24 <h2>Square Root of 6/5 by Long Division Method</h2>

23 <h2>Square Root of 6/5 by Long Division Method</h2>

25 <p>The<a>long division</a>method is particularly used for non-perfect square numbers.</p>

24 <p>The<a>long division</a>method is particularly used for non-perfect square numbers.</p>

26 <p>In this method, we should check the closest perfect square number for the given number.</p>

25 <p>In this method, we should check the closest perfect square number for the given number.</p>

27 <p>Let us now learn how to find the square root using the long division method, step by step.</p>

26 <p>Let us now learn how to find the square root using the long division method, step by step.</p>

28 <p><strong>Step 1:</strong>Express 6/5 as a<a>decimal</a>, which is 1.2.</p>

27 <p><strong>Step 1:</strong>Express 6/5 as a<a>decimal</a>, which is 1.2.</p>

29 <p><strong>Step 2:</strong>Group the<a>whole number</a>and decimal places appropriately. In this case, we start with 1.2.</p>

28 <p><strong>Step 2:</strong>Group the<a>whole number</a>and decimal places appropriately. In this case, we start with 1.2.</p>

30 <p><strong>Step 3:</strong>Find n whose square is closest to 1. The closest is 1, as 1 x 1 = 1.</p>

29 <p><strong>Step 3:</strong>Find n whose square is closest to 1. The closest is 1, as 1 x 1 = 1.</p>

31 <p><strong>Step 4:</strong>Subtract 1 from 1.2 to get 0.2 and bring down two zeros to get 20. The new<a>dividend</a>is 20.</p>

30 <p><strong>Step 4:</strong>Subtract 1 from 1.2 to get 0.2 and bring down two zeros to get 20. The new<a>dividend</a>is 20.</p>

32 <p><strong>Step 5:</strong>Double the<a>divisor</a>, which is 2.</p>

31 <p><strong>Step 5:</strong>Double the<a>divisor</a>, which is 2.</p>

33 <p><strong>Step 6:</strong>Find a number to place next to 2 to form a divisor that multiplied by the same number gives a product<a>less than</a>or equal to 20.</p>

32 <p><strong>Step 6:</strong>Find a number to place next to 2 to form a divisor that multiplied by the same number gives a product<a>less than</a>or equal to 20.</p>

34 <p><strong>Step 7:</strong>Continue the division to obtain the square root to the desired decimal places.</p>

33 <p><strong>Step 7:</strong>Continue the division to obtain the square root to the desired decimal places.</p>

35 <p>The square root of 6/5 or 1.2 is approximately 1.095.</p>

34 <p>The square root of 6/5 or 1.2 is approximately 1.095.</p>

36 <h2>Square Root of 6/5 by Approximation Method</h2>

35 <h2>Square Root of 6/5 by Approximation Method</h2>

37 <p>The approximation method is another way to find the square roots, especially for fractions.</p>

36 <p>The approximation method is another way to find the square roots, especially for fractions.</p>

38 <p>Let us learn how to find the square root of 6/5 using this method.</p>

37 <p>Let us learn how to find the square root of 6/5 using this method.</p>

39 <p><strong>Step 1:</strong>Convert the fraction to its decimal form, which is 1.2.</p>

38 <p><strong>Step 1:</strong>Convert the fraction to its decimal form, which is 1.2.</p>

40 <p><strong>Step 2:</strong>Identify the closest perfect squares. Since 1.2 is between 1 (1²) and 1.44 (1.2²), it falls between 1 and 1.2.</p>

39 <p><strong>Step 2:</strong>Identify the closest perfect squares. Since 1.2 is between 1 (1²) and 1.44 (1.2²), it falls between 1 and 1.2.</p>

41 <p><strong>Step 3:</strong>Use interpolation or approximation to find the square root. If 1.2 - 1 = 0.2 and 1.44 - 1 = 0.44, then the square root approximately equals 1 + (0.2/0.44) = 1.095.</p>

40 <p><strong>Step 3:</strong>Use interpolation or approximation to find the square root. If 1.2 - 1 = 0.2 and 1.44 - 1 = 0.44, then the square root approximately equals 1 + (0.2/0.44) = 1.095.</p>

42 <p>Therefore, the square root of 6/5 is approximately 1.095.</p>

41 <p>Therefore, the square root of 6/5 is approximately 1.095.</p>

43 <h2>Common Mistakes and How to Avoid Them in the Square Root of 6/5</h2>

42 <h2>Common Mistakes and How to Avoid Them in the Square Root of 6/5</h2>

44 <p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps.</p>

43 <p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps.</p>

45 <p>Here are a few common mistakes students make.</p>

44 <p>Here are a few common mistakes students make.</p>

46 <h3>Problem 1</h3>

45 <h3>Problem 1</h3>

47 <p>Can you help Max find the area of a square box if its side length is given as √(6/5)?</p>

46 <p>Can you help Max find the area of a square box if its side length is given as √(6/5)?</p>

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

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

49 <p>The area of the square is approximately 1.2 square units.</p>

48 <p>The area of the square is approximately 1.2 square units.</p>

50 <h3>Explanation</h3>

49 <h3>Explanation</h3>

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

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

52 <p>The side length is √(6/5).</p>

51 <p>The side length is √(6/5).</p>

53 <p>Area of the square = (√(6/5))²</p>

52 <p>Area of the square = (√(6/5))²</p>

54 <p>= 6/5</p>

53 <p>= 6/5</p>

55 <p>= 1.2</p>

54 <p>= 1.2</p>

56 <p>Therefore, the area of the square box is approximately 1.2 square units.</p>

55 <p>Therefore, the area of the square box is approximately 1.2 square units.</p>

57 <p>Well explained 👍</p>

56 <p>Well explained 👍</p>

58 <h3>Problem 2</h3>

57 <h3>Problem 2</h3>

59 <p>A square-shaped building measuring 6/5 square meters is built; if each of the sides is √(6/5), what will be the square meters of half of the building?</p>

58 <p>A square-shaped building measuring 6/5 square meters is built; if each of the sides is √(6/5), what will be the square meters of half of the building?</p>

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

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

61 <p>0.6 square meters</p>

60 <p>0.6 square meters</p>

62 <h3>Explanation</h3>

61 <h3>Explanation</h3>

63 <p>Since the building is square-shaped, we can divide the given area by 2.</p>

62 <p>Since the building is square-shaped, we can divide the given area by 2.</p>

64 <p>Dividing 6/5 by 2 = 0.6 So half of the building measures 0.6 square meters.</p>

63 <p>Dividing 6/5 by 2 = 0.6 So half of the building measures 0.6 square meters.</p>

65 <p>Well explained 👍</p>

64 <p>Well explained 👍</p>

66 <h3>Problem 3</h3>

65 <h3>Problem 3</h3>

67 <p>Calculate √(6/5) × 5.</p>

66 <p>Calculate √(6/5) × 5.</p>

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

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

69 <p>5.475</p>

68 <p>5.475</p>

70 <h3>Explanation</h3>

69 <h3>Explanation</h3>

71 <p>First, find the square root of 6/5, which is approximately 1.095.</p>

70 <p>First, find the square root of 6/5, which is approximately 1.095.</p>

72 <p>Then, multiply 1.095 by 5. So, 1.095 × 5 = 5.475</p>

71 <p>Then, multiply 1.095 by 5. So, 1.095 × 5 = 5.475</p>

73 <p>Well explained 👍</p>

72 <p>Well explained 👍</p>

74 <h3>Problem 4</h3>

73 <h3>Problem 4</h3>

75 <p>What will be the square root of (3 + 3/5)?</p>

74 <p>What will be the square root of (3 + 3/5)?</p>

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

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

77 <p>The square root is approximately 1.264</p>

76 <p>The square root is approximately 1.264</p>

78 <h3>Explanation</h3>

77 <h3>Explanation</h3>

79 <p>To find the square root, first find the sum of 3 + 3/5. 3 + 3/5 = 3.6, and then calculate √3.6 ≈ 1.897</p>

78 <p>To find the square root, first find the sum of 3 + 3/5. 3 + 3/5 = 3.6, and then calculate √3.6 ≈ 1.897</p>

80 <p>Therefore, the square root of (3 + 3/5) is approximately ±1.897</p>

79 <p>Therefore, the square root of (3 + 3/5) is approximately ±1.897</p>

81 <p>Well explained 👍</p>

80 <p>Well explained 👍</p>

82 <h3>Problem 5</h3>

81 <h3>Problem 5</h3>

83 <p>Find the perimeter of the rectangle if its length ‘l’ is √(6/5) units and the width ‘w’ is 3 units.</p>

82 <p>Find the perimeter of the rectangle if its length ‘l’ is √(6/5) units and the width ‘w’ is 3 units.</p>

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

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

85 <p>We find the perimeter of the rectangle as approximately 8.19 units.</p>

84 <p>We find the perimeter of the rectangle as approximately 8.19 units.</p>

86 <h3>Explanation</h3>

85 <h3>Explanation</h3>

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

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

88 <p>Perimeter = 2 × (√(6/5) + 3)</p>

87 <p>Perimeter = 2 × (√(6/5) + 3)</p>

89 <p>= 2 × (1.095 + 3)</p>

88 <p>= 2 × (1.095 + 3)</p>

90 <p>= 2 × 4.095</p>

89 <p>= 2 × 4.095</p>

91 <p>= 8.19 units.</p>

90 <p>= 8.19 units.</p>

92 <p>Well explained 👍</p>

91 <p>Well explained 👍</p>

93 <h2>FAQ on Square Root of 6/5</h2>

92 <h2>FAQ on Square Root of 6/5</h2>

94 <h3>1.What is √(6/5) in its simplest form?</h3>

93 <h3>1.What is √(6/5) in its simplest form?</h3>

95 <p>The simplest form of √(6/5) is √6/√5, which can be expressed as a decimal approximately equal to 1.095.</p>

94 <p>The simplest form of √(6/5) is √6/√5, which can be expressed as a decimal approximately equal to 1.095.</p>

96 <h3>2.What are the factors of 6 and 5?</h3>

95 <h3>2.What are the factors of 6 and 5?</h3>

97 <p>Factors of 6 are 1, 2, 3, and 6.</p>

96 <p>Factors of 6 are 1, 2, 3, and 6.</p>

98 <p>Factors of 5 are 1 and 5.</p>

97 <p>Factors of 5 are 1 and 5.</p>

99 <h3>3.Calculate the square of 6/5.</h3>

98 <h3>3.Calculate the square of 6/5.</h3>

100 <p>The square of 6/5 is (6/5) × (6/5) = 36/25 = 1.44.</p>

99 <p>The square of 6/5 is (6/5) × (6/5) = 36/25 = 1.44.</p>

101 <h3>4.Is 6/5 a prime number?</h3>

100 <h3>4.Is 6/5 a prime number?</h3>

102 <p>6/5 is not a prime number, as it is not an integer.</p>

101 <p>6/5 is not a prime number, as it is not an integer.</p>

103 <h3>5.Is 6/5 a rational number?</h3>

102 <h3>5.Is 6/5 a rational number?</h3>

104 <h2>Important Glossaries for the Square Root of 6/5</h2>

103 <h2>Important Glossaries for the Square Root of 6/5</h2>

105 <ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. Example: 4² = 16, and the inverse of the square is the square root, which is √16 = 4.</li>

104 <ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. Example: 4² = 16, and the inverse of the square is the square root, which is √16 = 4.</li>

106 <li><strong>Irrational number:</strong>An irrational number cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.</li>

105 <li><strong>Irrational number:</strong>An irrational number cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.</li>

107 <li><strong>Rational number:</strong>A rational number can be expressed as a ratio of two integers.</li>

106 <li><strong>Rational number:</strong>A rational number can be expressed as a ratio of two integers.</li>

108 <li><strong>Fraction:</strong>A fraction represents a part of a whole or any number of equal parts, expressed as a ratio of two numbers.</li>

107 <li><strong>Fraction:</strong>A fraction represents a part of a whole or any number of equal parts, expressed as a ratio of two numbers.</li>

109 <li><strong>Decimal:</strong>A decimal is a number that consists of a whole number and a fractional part separated by a decimal point, e.g., 7.86, 8.65, 9.42.</li>

108 <li><strong>Decimal:</strong>A decimal is a number that consists of a whole number and a fractional part separated by a decimal point, e.g., 7.86, 8.65, 9.42.</li>

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

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

111 <p>▶</p>

110 <p>▶</p>

112 <h2>Jaskaran Singh Saluja</h2>

111 <h2>Jaskaran Singh Saluja</h2>

113 <h3>About the Author</h3>

112 <h3>About the Author</h3>

114 <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>

113 <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>

115 <h3>Fun Fact</h3>

114 <h3>Fun Fact</h3>

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

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