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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 1/3.</p>

4 <h2>What is the Square Root of 1/3?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 1/3 is not a<a>perfect square</a>. The square root of 1/3 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √(1/3), whereas (1/3)^(1/2) in the exponential form. The square root of 1/3 is approximately 0.57735, 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 1/3</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 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 1/3 by Long Division Method</h2>

12 <p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>of 1/3 using the long division method, step by step:</p>

13 <p><strong>Step 1:</strong>To begin with, we consider 1/3, which is 0.333...</p>

14 <p><strong>Step 2:</strong>Estimate a number close to 0.333... whose square is<a>less than</a>or equal to this number. We start with 0.5 since 0.5^2 = 0.25.</p>

15 <p><strong>Step 3:</strong>Improve the approximation by using the long division method to find a more accurate value.</p>

16 <p><strong>Step 4:</strong>Continue the long division steps to find more precise<a>decimal</a>places.</p>

17 <p>The square root of 1/3 is approximately 0.57735.</p>

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20 <h2>Square Root of 1/3 by Approximation Method</h2>

19 <h2>Square Root of 1/3 by Approximation Method</h2>

21 <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 1/3 using the approximation method.</p>

20 <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 1/3 using the approximation method.</p>

22 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares around 1/3. The closest perfect squares to 1/3 are 0.25 (which is 0.5^2) and 0.5625 (which is 0.75^2). The square root of 1/3 falls somewhere between 0.5 and 0.75.</p>

21 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares around 1/3. The closest perfect squares to 1/3 are 0.25 (which is 0.5^2) and 0.5625 (which is 0.75^2). The square root of 1/3 falls somewhere between 0.5 and 0.75.</p>

23 <p><strong>Step 2:</strong>Apply the<a>formula</a>for linear approximation between these two points. Using the approximation method, we conclude the square root of 1/3 is approximately 0.57735.</p>

22 <p><strong>Step 2:</strong>Apply the<a>formula</a>for linear approximation between these two points. Using the approximation method, we conclude the square root of 1/3 is approximately 0.57735.</p>

24 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1/3</h2>

23 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1/3</h2>

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

24 <p>Students make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in methods. Now let us look at a few of those mistakes that students tend to make 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 √(1/6)?</p>

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

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

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

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

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

30 <h3>Explanation</h3>

29 <h3>Explanation</h3>

31 <p>The area of the square = side^2.</p>

30 <p>The area of the square = side^2.</p>

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

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

33 <p>Area of the square = (√(1/6))^2 = 1/6 ≈ 0.1667.</p>

32 <p>Area of the square = (√(1/6))^2 = 1/6 ≈ 0.1667.</p>

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

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

35 <p>Well explained 👍</p>

34 <p>Well explained 👍</p>

36 <h3>Problem 2</h3>

35 <h3>Problem 2</h3>

37 <p>A square-shaped building measuring 1/3 square feet is built; if each of the sides is √(1/3), what will be the square feet of half of the building?</p>

36 <p>A square-shaped building measuring 1/3 square feet is built; if each of the sides is √(1/3), what will be the square feet of half of the building?</p>

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

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

39 <p>0.1667 square feet</p>

38 <p>0.1667 square feet</p>

40 <h3>Explanation</h3>

39 <h3>Explanation</h3>

41 <p>We can just divide the given area by 2 as the building is square-shaped.</p>

40 <p>We can just divide the given area by 2 as the building is square-shaped.</p>

42 <p>Dividing 1/3 by 2 = 1/6 ≈ 0.1667.</p>

41 <p>Dividing 1/3 by 2 = 1/6 ≈ 0.1667.</p>

43 <p>So half of the building measures approximately 0.1667 square feet.</p>

42 <p>So half of the building measures approximately 0.1667 square feet.</p>

44 <p>Well explained 👍</p>

43 <p>Well explained 👍</p>

45 <h3>Problem 3</h3>

44 <h3>Problem 3</h3>

46 <p>Calculate √(1/3) × 5.</p>

45 <p>Calculate √(1/3) × 5.</p>

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

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

48 <p>Approximately 2.88675</p>

47 <p>Approximately 2.88675</p>

49 <h3>Explanation</h3>

48 <h3>Explanation</h3>

50 <p>The first step is to find the square root of 1/3, which is approximately 0.57735.</p>

49 <p>The first step is to find the square root of 1/3, which is approximately 0.57735.</p>

51 <p>The second step is to multiply 0.57735 by 5.</p>

50 <p>The second step is to multiply 0.57735 by 5.</p>

52 <p>So, 0.57735 × 5 ≈ 2.88675.</p>

51 <p>So, 0.57735 × 5 ≈ 2.88675.</p>

53 <p>Well explained 👍</p>

52 <p>Well explained 👍</p>

54 <h3>Problem 4</h3>

53 <h3>Problem 4</h3>

55 <p>What will be the square root of (1/6 + 1/12)?</p>

54 <p>What will be the square root of (1/6 + 1/12)?</p>

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

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

57 <p>Approximately 0.6455</p>

56 <p>Approximately 0.6455</p>

58 <h3>Explanation</h3>

57 <h3>Explanation</h3>

59 <p>To find the square root, first find (1/6 + 1/12).</p>

58 <p>To find the square root, first find (1/6 + 1/12).</p>

60 <p>1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4.</p>

59 <p>1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4.</p>

61 <p>The square root of 1/4 is 1/2 = 0.5.</p>

60 <p>The square root of 1/4 is 1/2 = 0.5.</p>

62 <p>Therefore, the square root of (1/6 + 1/12) is 0.5.</p>

61 <p>Therefore, the square root of (1/6 + 1/12) is 0.5.</p>

63 <p>Well explained 👍</p>

62 <p>Well explained 👍</p>

64 <h3>Problem 5</h3>

63 <h3>Problem 5</h3>

65 <p>Find the perimeter of the rectangle if its length ‘l’ is √(1/3) units and the width ‘w’ is 1 unit.</p>

64 <p>Find the perimeter of the rectangle if its length ‘l’ is √(1/3) units and the width ‘w’ is 1 unit.</p>

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

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

67 <p>Approximately 3.1547 units.</p>

66 <p>Approximately 3.1547 units.</p>

68 <h3>Explanation</h3>

67 <h3>Explanation</h3>

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

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

70 <p>Perimeter = 2 × (√(1/3) + 1) = 2 × (0.57735 + 1) ≈ 2 × 1.57735 ≈ 3.1547 units.</p>

69 <p>Perimeter = 2 × (√(1/3) + 1) = 2 × (0.57735 + 1) ≈ 2 × 1.57735 ≈ 3.1547 units.</p>

71 <p>Well explained 👍</p>

70 <p>Well explained 👍</p>

72 <h2>FAQ on Square Root of 1/3</h2>

71 <h2>FAQ on Square Root of 1/3</h2>

73 <h3>1.What is √(1/3) in its simplest form?</h3>

72 <h3>1.What is √(1/3) in its simplest form?</h3>

74 <p>The simplest form of √(1/3) is √(1)/√(3), which can be rationalized to 1/√(3) × √(3)/√(3) = √(3)/3.</p>

73 <p>The simplest form of √(1/3) is √(1)/√(3), which can be rationalized to 1/√(3) × √(3)/√(3) = √(3)/3.</p>

75 <h3>2.Is 1/3 an irrational number?</h3>

74 <h3>2.Is 1/3 an irrational number?</h3>

76 <h3>3.Calculate the square of 1/3.</h3>

75 <h3>3.Calculate the square of 1/3.</h3>

77 <p>The square of 1/3 is (1/3) × (1/3) = 1/9.</p>

76 <p>The square of 1/3 is (1/3) × (1/3) = 1/9.</p>

78 <h3>4.Is 1/3 a prime number?</h3>

77 <h3>4.Is 1/3 a prime number?</h3>

79 <h3>5.What is the reciprocal of 1/3?</h3>

78 <h3>5.What is the reciprocal of 1/3?</h3>

80 <p>The reciprocal of 1/3 is 3.</p>

79 <p>The reciprocal of 1/3 is 3.</p>

81 <h2>Important Glossaries for the Square Root of 1/3</h2>

80 <h2>Important Glossaries for the Square Root of 1/3</h2>

82 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 2^2 = 4 and the inverse of the square is the square root, √4 = 2.</li>

81 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 2^2 = 4 and the inverse of the square is the square root, √4 = 2.</li>

83 </ul><ul><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>

82 </ul><ul><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>

84 </ul><ul><li><strong>Rational number:</strong>A rational number can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero.</li>

83 </ul><ul><li><strong>Rational number:</strong>A rational number can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero.</li>

85 </ul><ul><li><strong>Reciprocal:</strong>The reciprocal of a number is 1 divided by that number. For example, the reciprocal of 1/3 is 3.</li>

84 </ul><ul><li><strong>Reciprocal:</strong>The reciprocal of a number is 1 divided by that number. For example, the reciprocal of 1/3 is 3.</li>

86 </ul><ul><li><strong>Approximation:</strong>Approximation is the process of finding a value that is close to but not exactly equal to the actual value, often used for irrational numbers.</li>

85 </ul><ul><li><strong>Approximation:</strong>Approximation is the process of finding a value that is close to but not exactly equal to the actual value, often used for irrational numbers.</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>