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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. Square roots are used in various fields such as engineering, finance, and physics. Here, we will discuss the square root of 1/8.</p>

4 <h2>What is the Square Root of 1/8?</h2>

5 <p>The<a>square</a>root is the inverse operation of squaring a<a>number</a>. 1/8 is a<a>fraction</a>, and its square root can be expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √(1/8), whereas in exponential form it is (1/8)^(1/2). The value of √(1/8) is approximately 0.35355, which is an<a>irrational number</a>because it cannot be expressed as a simple fraction of<a>integers</a>.</p>

6 <h2>Finding the Square Root of 1/8</h2>

7 <p>For fractions, the<a>square root</a>can be found directly. However, for non-<a>perfect squares</a>, approximation methods may be used. Let us now discuss the following methods:</p>

8 <ul><li>Direct calculation method</li>

9 <li>Approximation method</li>

10 </ul><h2>Square Root of 1/8 by Direct Calculation</h2>

11 <p>To find the square root of a fraction like 1/8, you can take the square roots of the<a>numerator</a>and the<a>denominator</a>separately:</p>

12 <p><strong>Step 1:</strong>Square root of the numerator: √1 = 1</p>

13 <p><strong>Step 2:</strong>Square root of the denominator: √8 = √(4 × 2) = 2√2</p>

14 <p><strong>Step 3:</strong>Combine the results: √(1/8) = 1/(2√2)</p>

15 <p><strong>Step 4:</strong>Simplify if necessary: Multiply<a>numerator and denominator</a>by √2 to<a>rationalize</a>the denominator: 1/(2√2) × √2/√2 = √2/4</p>

16 <p>Thus, the square root of 1/8 is √2/4.</p>

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19 <h2>Square Root of 1/8 by Approximation Method</h2>

18 <h2>Square Root of 1/8 by Approximation Method</h2>

20 <p>The approximation method can be used to find the square root of a fraction. For √(1/8), we first convert it to a<a>decimal</a>and then find its square root.</p>

19 <p>The approximation method can be used to find the square root of a fraction. For √(1/8), we first convert it to a<a>decimal</a>and then find its square root.</p>

21 <p><strong>Step 1:</strong>Convert 1/8 to a decimal: 1/8 = 0.125</p>

20 <p><strong>Step 1:</strong>Convert 1/8 to a decimal: 1/8 = 0.125</p>

22 <p><strong>Step 2:</strong>Use a<a>calculator</a>or estimate the square root of 0.125, which is approximately 0.35355.</p>

21 <p><strong>Step 2:</strong>Use a<a>calculator</a>or estimate the square root of 0.125, which is approximately 0.35355.</p>

23 <p>Therefore, the approximate square root of 1/8 is 0.35355.</p>

22 <p>Therefore, the approximate square root of 1/8 is 0.35355.</p>

24 <h2>Common Mistakes and How to Avoid Them in Finding the Square Root of 1/8</h2>

23 <h2>Common Mistakes and How to Avoid Them in Finding the Square Root of 1/8</h2>

25 <p>Students often make errors while finding square roots, such as misunderstanding the properties of fractions or failing to rationalize denominators. Let's look at a few common mistakes in detail.</p>

24 <p>Students often make errors while finding square roots, such as misunderstanding the properties of fractions or failing to rationalize denominators. Let's look at a few common mistakes in detail.</p>

26 <h3>Problem 1</h3>

25 <h3>Problem 1</h3>

27 <p>Can you help Max find the area of a square box if its side length is given as √(1/8)?</p>

26 <p>Can you help Max find the area of a square box if its side length is given as √(1/8)?</p>

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

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

29 <p>The area of the square is 1/8 square units.</p>

28 <p>The area of the square is 1/8 square units.</p>

30 <h3>Explanation</h3>

29 <h3>Explanation</h3>

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

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

32 <p>The side length is given as √(1/8).</p>

31 <p>The side length is given as √(1/8).</p>

33 <p>Area of the square = (√(1/8))²</p>

32 <p>Area of the square = (√(1/8))²</p>

34 <p>= 1/8.</p>

33 <p>= 1/8.</p>

35 <p>Therefore, the area of the square box is 1/8 square units.</p>

34 <p>Therefore, the area of the square box is 1/8 square units.</p>

36 <p>Well explained 👍</p>

35 <p>Well explained 👍</p>

37 <h3>Problem 2</h3>

36 <h3>Problem 2</h3>

38 <p>A square-shaped plot measures 1/8 of a square meter. What is the side length of the plot?</p>

37 <p>A square-shaped plot measures 1/8 of a square meter. What is the side length of the plot?</p>

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

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

40 <p>The side length of the plot is √(1/8) meters.</p>

39 <p>The side length of the plot is √(1/8) meters.</p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>For a square plot, the side length is the square root of the area. Side length = √(1/8) meters.</p>

41 <p>For a square plot, the side length is the square root of the area. Side length = √(1/8) meters.</p>

43 <p>Well explained 👍</p>

42 <p>Well explained 👍</p>

44 <h3>Problem 3</h3>

43 <h3>Problem 3</h3>

45 <p>Calculate √(1/8) × 4.</p>

44 <p>Calculate √(1/8) × 4.</p>

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

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

47 <p>The result is √2/2 or approximately 1.4142.</p>

46 <p>The result is √2/2 or approximately 1.4142.</p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>First, find the square root of 1/8, which is √2/4.</p>

48 <p>First, find the square root of 1/8, which is √2/4.</p>

50 <p>Then multiply by 4. (√2/4) × 4 = √2.</p>

49 <p>Then multiply by 4. (√2/4) × 4 = √2.</p>

51 <p>Well explained 👍</p>

50 <p>Well explained 👍</p>

52 <h3>Problem 4</h3>

51 <h3>Problem 4</h3>

53 <p>What is the square root of (1/4 + 1/8)?</p>

52 <p>What is the square root of (1/4 + 1/8)?</p>

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

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

55 <p>The square root is √(3/8).</p>

54 <p>The square root is √(3/8).</p>

56 <h3>Explanation</h3>

55 <h3>Explanation</h3>

57 <p>First, find the sum: 1/4 + 1/8 = 2/8 + 1/8 = 3/8.</p>

56 <p>First, find the sum: 1/4 + 1/8 = 2/8 + 1/8 = 3/8.</p>

58 <p>Then, take the square root: √(3/8).</p>

57 <p>Then, take the square root: √(3/8).</p>

59 <p>Well explained 👍</p>

58 <p>Well explained 👍</p>

60 <h3>Problem 5</h3>

59 <h3>Problem 5</h3>

61 <p>Find the perimeter of a rectangle if its length ‘l’ is √(1/8) units and the width ‘w’ is 1 unit.</p>

60 <p>Find the perimeter of a rectangle if its length ‘l’ is √(1/8) units and the width ‘w’ is 1 unit.</p>

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

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

63 <p>The perimeter of the rectangle is approximately 2.7071 units.</p>

62 <p>The perimeter of the rectangle is approximately 2.7071 units.</p>

64 <h3>Explanation</h3>

63 <h3>Explanation</h3>

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

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

66 <p>Perimeter = 2 × (√(1/8) + 1)</p>

65 <p>Perimeter = 2 × (√(1/8) + 1)</p>

67 <p>= 2 × (0.35355 + 1)</p>

66 <p>= 2 × (0.35355 + 1)</p>

68 <p>≈ 2.7071 units.</p>

67 <p>≈ 2.7071 units.</p>

69 <p>Well explained 👍</p>

68 <p>Well explained 👍</p>

70 <h2>FAQ on Square Root of 1/8</h2>

69 <h2>FAQ on Square Root of 1/8</h2>

71 <h3>1.What is √(1/8) in its simplest form?</h3>

70 <h3>1.What is √(1/8) in its simplest form?</h3>

72 <p>√(1/8) can be expressed as √2/4 in its simplest form.</p>

71 <p>√(1/8) can be expressed as √2/4 in its simplest form.</p>

73 <h3>2.Is 1/8 a perfect square?</h3>

72 <h3>2.Is 1/8 a perfect square?</h3>

74 <p>1/8 is not a perfect square because it cannot be expressed as the square of a<a>rational number</a>.</p>

73 <p>1/8 is not a perfect square because it cannot be expressed as the square of a<a>rational number</a>.</p>

75 <h3>3.What is the decimal value of √(1/8)?</h3>

74 <h3>3.What is the decimal value of √(1/8)?</h3>

76 <p>The decimal value of √(1/8) is approximately 0.35355.</p>

75 <p>The decimal value of √(1/8) is approximately 0.35355.</p>

77 <h3>4.How do you rationalize the denominator of √(1/8)?</h3>

76 <h3>4.How do you rationalize the denominator of √(1/8)?</h3>

78 <p>To rationalize the denominator of √(1/8), you multiply by √2/√2, resulting in √2/4.</p>

77 <p>To rationalize the denominator of √(1/8), you multiply by √2/√2, resulting in √2/4.</p>

79 <h3>5.Is √(1/8) an irrational number?</h3>

78 <h3>5.Is √(1/8) an irrational number?</h3>

80 <p>Yes, √(1/8) is an irrational number because it cannot be expressed as a simple fraction of integers.</p>

79 <p>Yes, √(1/8) is an irrational number because it cannot be expressed as a simple fraction of integers.</p>

81 <h2>Important Glossaries for the Square Root of 1/8</h2>

80 <h2>Important Glossaries for the Square Root of 1/8</h2>

82 <ul><li><strong>Square root:</strong>A square root is a value that, when multiplied by itself, gives the original number. For example, √4 = 2 because 2 × 2 = 4. </li>

81 <ul><li><strong>Square root:</strong>A square root is a value that, when multiplied by itself, gives the original number. For example, √4 = 2 because 2 × 2 = 4. </li>

83 <li><strong>Rationalization:</strong>Rationalization is the process of eliminating a radical from the denominator of a fraction. </li>

82 <li><strong>Rationalization:</strong>Rationalization is the process of eliminating a radical from the denominator of a fraction. </li>

84 <li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction, such as √2. </li>

83 <li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction, such as √2. </li>

85 <li><strong>Fraction:</strong>A fraction represents a part of a whole and consists of a numerator and a denominator. </li>

84 <li><strong>Fraction:</strong>A fraction represents a part of a whole and consists of a numerator and a denominator. </li>

86 <li><strong>Decimal:</strong>A decimal is a number that includes a decimal point to represent a fraction, such as 0.5, which is equivalent to 1/2.</li>

85 <li><strong>Decimal:</strong>A decimal is a number that includes a decimal point to represent a fraction, such as 0.5, which is equivalent to 1/2.</li>

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

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

88 <p>▶</p>

87 <p>▶</p>

89 <h2>Jaskaran Singh Saluja</h2>

88 <h2>Jaskaran Singh Saluja</h2>

90 <h3>About the Author</h3>

89 <h3>About the Author</h3>

91 <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>

90 <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>

92 <h3>Fun Fact</h3>

91 <h3>Fun Fact</h3>

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

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