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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 1/6.</p>

4 <h2>What is the Square Root of 1/6?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 1/6 is not a<a>perfect square</a>. The square root of 1/6 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √(1/6), whereas (1/6)^(1/2) in exponential form. √(1/6) = 0.40825, 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>

6 <h2>Finding the Square Root of 1/6</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>

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

9 <li>Long division method</li>

10 <li>Approximation method</li>

11 </ul><h2>Square Root of 1/6 by Prime Factorization Method</h2>

12 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Since 1/6 is a<a>fraction</a>, we need to consider the prime factorization of 6.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 6 Breaking it down, we get 2 x 3.</p>

14 <p><strong>Step 2:</strong>Now we found out the prime factors of 6. Since 1/6 is not a perfect square, calculating √(1/6) using prime factorization requires rewriting it as a fraction of two square roots: √1/√6.</p>

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17 <h2>Square Root of 1/6 by Long Division Method</h2>

16 <h2>Square Root of 1/6 by Long Division Method</h2>

18 <p>The<a>long division</a>method is particularly used for non-perfect square numbers. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>

17 <p>The<a>long division</a>method is particularly used for non-perfect square numbers. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>

19 <p><strong>Step 1:</strong>To begin with, let's find the square root of 1 and 6 separately.</p>

18 <p><strong>Step 1:</strong>To begin with, let's find the square root of 1 and 6 separately.</p>

20 <p><strong>Step 2:</strong>√1 is 1.</p>

19 <p><strong>Step 2:</strong>√1 is 1.</p>

21 <p><strong>Step 3:</strong>Using the long division method or a<a>calculator</a>, find the square root of 6, which is approximately 2.44949.</p>

20 <p><strong>Step 3:</strong>Using the long division method or a<a>calculator</a>, find the square root of 6, which is approximately 2.44949.</p>

22 <p><strong>Step 4:</strong>Now, divide 1 by 2.44949 to get the square root of 1/6.</p>

21 <p><strong>Step 4:</strong>Now, divide 1 by 2.44949 to get the square root of 1/6.</p>

23 <p><strong>Step 5:</strong>The result is approximately 0.40825.</p>

22 <p><strong>Step 5:</strong>The result is approximately 0.40825.</p>

24 <h2>Square Root of 1/6 by Approximation Method</h2>

23 <h2>Square Root of 1/6 by Approximation Method</h2>

25 <p>The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 1/6 using the approximation method.</p>

24 <p>The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 1/6 using the approximation method.</p>

26 <p><strong>Step 1:</strong>We already know that √1 is 1.</p>

25 <p><strong>Step 1:</strong>We already know that √1 is 1.</p>

27 <p><strong>Step 2:</strong>We find that the square root of 6 is approximately 2.44949.</p>

26 <p><strong>Step 2:</strong>We find that the square root of 6 is approximately 2.44949.</p>

28 <p><strong>Step 3:</strong>Dividing 1 by 2.44949 gives us approximately 0.40825, which is the square root of 1/6.</p>

27 <p><strong>Step 3:</strong>Dividing 1 by 2.44949 gives us approximately 0.40825, which is the square root of 1/6.</p>

29 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1/6</h2>

28 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1/6</h2>

30 <p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of those mistakes that students tend to make in detail.</p>

29 <p>Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of those mistakes that students tend to make in detail.</p>

31 <h3>Problem 1</h3>

30 <h3>Problem 1</h3>

32 <p>Can you help Max find the area of a square box if its side length is given as √(1/6)?</p>

31 <p>Can you help Max find the area of a square box if its side length is given as √(1/6)?</p>

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

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

34 <p>The area of the square is approximately 0.1667 square units.</p>

33 <p>The area of the square is approximately 0.1667 square units.</p>

35 <h3>Explanation</h3>

34 <h3>Explanation</h3>

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

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

37 <p>The side length is given as √(1/6).</p>

36 <p>The side length is given as √(1/6).</p>

38 <p>Area of the square = side²</p>

37 <p>Area of the square = side²</p>

39 <p>= (√(1/6))²</p>

38 <p>= (√(1/6))²</p>

40 <p>= 1/6</p>

39 <p>= 1/6</p>

41 <p>≈ 0.1667.</p>

40 <p>≈ 0.1667.</p>

42 <p>Therefore, the area of the square box is approximately 0.1667 square units.</p>

41 <p>Therefore, the area of the square box is approximately 0.1667 square units.</p>

43 <p>Well explained 👍</p>

42 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

43 <h3>Problem 2</h3>

45 <p>A rectangle measures 1/6 square feet in area. If one side is √2 feet, what is the length of the other side?</p>

44 <p>A rectangle measures 1/6 square feet in area. If one side is √2 feet, what is the length of the other side?</p>

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

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

47 <p>The length of the other side is approximately 0.2041 feet.</p>

46 <p>The length of the other side is approximately 0.2041 feet.</p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>Using the area formula for a rectangle, Area = length × width.</p>

48 <p>Using the area formula for a rectangle, Area = length × width.</p>

50 <p>Given Area = 1/6 and one side (width) = √2,</p>

49 <p>Given Area = 1/6 and one side (width) = √2,</p>

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

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

52 <p>= (1/6)/√2</p>

51 <p>= (1/6)/√2</p>

53 <p>= √(1/6)</p>

52 <p>= √(1/6)</p>

54 <p>= 0.40825.</p>

53 <p>= 0.40825.</p>

55 <p>Dividing gives approximately 0.2041 feet for the other side.</p>

54 <p>Dividing gives approximately 0.2041 feet for the other side.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 3</h3>

56 <h3>Problem 3</h3>

58 <p>Calculate √(1/6) x 10.</p>

57 <p>Calculate √(1/6) x 10.</p>

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

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

60 <p>Approximately 4.0825</p>

59 <p>Approximately 4.0825</p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>The first step is to find the square root of 1/6, which is approximately 0.40825.</p>

61 <p>The first step is to find the square root of 1/6, which is approximately 0.40825.</p>

63 <p>The second step is to multiply 0.40825 with 10.</p>

62 <p>The second step is to multiply 0.40825 with 10.</p>

64 <p>So 0.40825 × 10 = 4.0825.</p>

63 <p>So 0.40825 × 10 = 4.0825.</p>

65 <p>Well explained 👍</p>

64 <p>Well explained 👍</p>

66 <h3>Problem 4</h3>

65 <h3>Problem 4</h3>

67 <p>What will be the square root of (1/6 + 1/3)?</p>

66 <p>What will be the square root of (1/6 + 1/3)?</p>

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

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

69 <p>The square root is approximately 0.5774.</p>

68 <p>The square root is approximately 0.5774.</p>

70 <h3>Explanation</h3>

69 <h3>Explanation</h3>

71 <p>To find the square root, we need to find the sum of (1/6 + 1/3).</p>

70 <p>To find the square root, we need to find the sum of (1/6 + 1/3).</p>

72 <p>1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 0.5, and then the square root of 0.5 ≈ 0.7071.</p>

71 <p>1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 0.5, and then the square root of 0.5 ≈ 0.7071.</p>

73 <p>Therefore, the square root of (1/6 + 1/3) is approximately ±0.7071.</p>

72 <p>Therefore, the square root of (1/6 + 1/3) is approximately ±0.7071.</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 √2 units and the width 'w' is √(1/6) units.</p>

75 <p>Find the perimeter of a rectangle if its length 'l' is √2 units and the width 'w' is √(1/6) units.</p>

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

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

78 <p>The perimeter of the rectangle is approximately 5.6325 units.</p>

77 <p>The perimeter of the rectangle is approximately 5.6325 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 × (√2 + √(1/6))</p>

80 <p>Perimeter = 2 × (√2 + √(1/6))</p>

82 <p>≈ 2 × (1.4142 + 0.40825)</p>

81 <p>≈ 2 × (1.4142 + 0.40825)</p>

83 <p>= 2 × 1.82245</p>

82 <p>= 2 × 1.82245</p>

84 <p>≈ 5.6325 units.</p>

83 <p>≈ 5.6325 units.</p>

85 <p>Well explained 👍</p>

84 <p>Well explained 👍</p>

86 <h2>FAQ on Square Root of 1/6</h2>

85 <h2>FAQ on Square Root of 1/6</h2>

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

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

88 <p>√(1/6) can be written as √1/√6. Since 1 is a perfect square, √1 = 1, so the simplest form is 1/√6.</p>

87 <p>√(1/6) can be written as √1/√6. Since 1 is a perfect square, √1 = 1, so the simplest form is 1/√6.</p>

89 <h3>2.What is the decimal value of √(1/6)?</h3>

88 <h3>2.What is the decimal value of √(1/6)?</h3>

90 <p>The<a>decimal</a>value of √(1/6) is approximately 0.40825.</p>

89 <p>The<a>decimal</a>value of √(1/6) is approximately 0.40825.</p>

91 <h3>3.Calculate the square of 1/6.</h3>

90 <h3>3.Calculate the square of 1/6.</h3>

92 <p>We get the square of 1/6 by multiplying the number by itself, that is (1/6) × (1/6) = 1/36.</p>

91 <p>We get the square of 1/6 by multiplying the number by itself, that is (1/6) × (1/6) = 1/36.</p>

93 <h3>4.Is 1/6 a rational number?</h3>

92 <h3>4.Is 1/6 a rational number?</h3>

94 <p>Yes, 1/6 is a<a>rational number</a>because it can be expressed as p/q, where p and q are integers and q ≠ 0.</p>

93 <p>Yes, 1/6 is a<a>rational number</a>because it can be expressed as p/q, where p and q are integers and q ≠ 0.</p>

95 <h3>5.What numbers are used to express 1/6 in terms of its prime factors?</h3>

94 <h3>5.What numbers are used to express 1/6 in terms of its prime factors?</h3>

96 <p>The number 6 can be expressed in<a>terms</a>of its prime factors as 2 × 3. Therefore, 1/6 in terms of prime factors involves 1/(2 × 3).</p>

95 <p>The number 6 can be expressed in<a>terms</a>of its prime factors as 2 × 3. Therefore, 1/6 in terms of prime factors involves 1/(2 × 3).</p>

97 <h2>Important Glossaries for the Square Root of 1/6</h2>

96 <h2>Important Glossaries for the Square Root of 1/6</h2>

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

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

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

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

100 <li><strong>Fraction:</strong>A fraction represents a part of a whole or, more generally, any number of equal parts. It is represented as a ratio of two integers, for example, 1/6. </li>

99 <li><strong>Fraction:</strong>A fraction represents a part of a whole or, more generally, any number of equal parts. It is represented as a ratio of two integers, for example, 1/6. </li>

101 <li><strong>Decimal approximation:</strong>This is an approximate representation of a number in decimal form. For example, the square root of 1/6 is approximately 0.40825. </li>

100 <li><strong>Decimal approximation:</strong>This is an approximate representation of a number in decimal form. For example, the square root of 1/6 is approximately 0.40825. </li>

102 <li><strong>Perimeter:</strong>The perimeter is the distance around a two-dimensional shape. For a rectangle, it is calculated as 2 × (length + width).</li>

101 <li><strong>Perimeter:</strong>The perimeter is the distance around a two-dimensional shape. For a rectangle, it is calculated as 2 × (length + width).</li>

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

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

104 <p>▶</p>

103 <p>▶</p>

105 <h2>Jaskaran Singh Saluja</h2>

104 <h2>Jaskaran Singh Saluja</h2>

106 <h3>About the Author</h3>

105 <h3>About the Author</h3>

107 <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 <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>

108 <h3>Fun Fact</h3>

107 <h3>Fun Fact</h3>

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

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