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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 various fields such as engineering, physics, and statistics. Here, we will discuss the square root of 4/3.</p>

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

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 4/3 is not a<a>perfect square</a>. The square root of 4/3 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √(4/3), whereas (4/3)^(1/2) in the exponential form. √(4/3) = √4/√3 = 2/√3, which can also be expressed as (2√3)/3 when rationalized. This 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 4/3</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect squares like 4/3, the simplifying radical and<a>rationalization</a>method are used. Let us now learn these methods:</p>

8 <ul><li>Simplifying radical form</li>

9 <li>Rationalization</li>

10 </ul><h2>Square Root of 4/3 by Simplifying Radical Form</h2>

11 <p>To simplify the<a>square root</a>of a<a>fraction</a>, we find the square roots of the<a>numerator</a>and the<a>denominator</a>separately.</p>

12 <p><strong>Step 1:</strong>Identify the square root of the numerator, √4, which is 2.</p>

13 <p><strong>Step 2:</strong>Identify the square root of the denominator, √3, which remains √3 because 3 is not a perfect square.</p>

14 <p><strong>Step 3:</strong>Combine these results as a fraction, resulting in √(4/3) = 2/√3.</p>

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17 <h2>Square Root of 4/3 by Rationalization</h2>

16 <h2>Square Root of 4/3 by Rationalization</h2>

18 <p>Rationalization involves eliminating the radical from the denominator.</p>

17 <p>Rationalization involves eliminating the radical from the denominator.</p>

19 <p><strong>Step 1:</strong>Start with the fraction 2/√3.</p>

18 <p><strong>Step 1:</strong>Start with the fraction 2/√3.</p>

20 <p><strong>Step 2:</strong>Multiply both the numerator and the denominator by √3 to eliminate the radical from the denominator.</p>

19 <p><strong>Step 2:</strong>Multiply both the numerator and the denominator by √3 to eliminate the radical from the denominator.</p>

21 <p><strong>Step 3:</strong>This results in (2√3)/(√3 × √3) = (2√3)/3.</p>

20 <p><strong>Step 3:</strong>This results in (2√3)/(√3 × √3) = (2√3)/3.</p>

22 <h2>Common Mistakes and How to Avoid Them in the Square Root of 4/3</h2>

21 <h2>Common Mistakes and How to Avoid Them in the Square Root of 4/3</h2>

23 <p>Students often make mistakes when dealing with square roots, such as forgetting to<a>rationalize</a>or misapplying the properties of radicals. Let's explore some of these errors in detail.</p>

22 <p>Students often make mistakes when dealing with square roots, such as forgetting to<a>rationalize</a>or misapplying the properties of radicals. Let's explore some of these errors in detail.</p>

24 <h3>Problem 1</h3>

23 <h3>Problem 1</h3>

25 <p>Can you help Max find the length of the diagonal of a square if its side length is √(4/3)?</p>

24 <p>Can you help Max find the length of the diagonal of a square if its side length is √(4/3)?</p>

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

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

27 <p>The diagonal of the square is approximately 2.309401 units.</p>

26 <p>The diagonal of the square is approximately 2.309401 units.</p>

28 <h3>Explanation</h3>

27 <h3>Explanation</h3>

29 <p>The diagonal of a square can be found using the formula √2 × side length.</p>

28 <p>The diagonal of a square can be found using the formula √2 × side length.</p>

30 <p>The side length is √(4/3).</p>

29 <p>The side length is √(4/3).</p>

31 <p>Diagonal = √2 × √(4/3) = √(8/3) = 2√(2/3) ≈ 2.309401.</p>

30 <p>Diagonal = √2 × √(4/3) = √(8/3) = 2√(2/3) ≈ 2.309401.</p>

32 <p>Well explained 👍</p>

31 <p>Well explained 👍</p>

33 <h3>Problem 2</h3>

32 <h3>Problem 2</h3>

34 <p>A rectangular field has an area of 4/3 square meters, with the length being twice the square root of 4/3. What is the width?</p>

33 <p>A rectangular field has an area of 4/3 square meters, with the length being twice the square root of 4/3. What is the width?</p>

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

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

36 <p>The width is approximately 0.57735 meters.</p>

35 <p>The width is approximately 0.57735 meters.</p>

37 <h3>Explanation</h3>

36 <h3>Explanation</h3>

38 <p>Let the width be 'w'.</p>

37 <p>Let the width be 'w'.</p>

39 <p>Area = length × width = (2 × √(4/3)) × w = 4/3.</p>

38 <p>Area = length × width = (2 × √(4/3)) × w = 4/3.</p>

40 <p>w = (4/3) / (2 × √(4/3)) = 1/(2√(4/3)) = 1/((4√3)/3) = √3/4. Width ≈ 0.57735 meters.</p>

39 <p>w = (4/3) / (2 × √(4/3)) = 1/(2√(4/3)) = 1/((4√3)/3) = √3/4. Width ≈ 0.57735 meters.</p>

41 <p>Well explained 👍</p>

40 <p>Well explained 👍</p>

42 <h3>Problem 3</h3>

41 <h3>Problem 3</h3>

43 <p>Calculate √(4/3) × 6.</p>

42 <p>Calculate √(4/3) × 6.</p>

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

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

45 <p>Approximately 4.6188.</p>

44 <p>Approximately 4.6188.</p>

46 <h3>Explanation</h3>

45 <h3>Explanation</h3>

47 <p>First, find the square root of 4/3 which is (2√3)/3.</p>

46 <p>First, find the square root of 4/3 which is (2√3)/3.</p>

48 <p>√(4/3) × 6 = (2√3)/3 × 6 = 4√3 ≈ 4.6188.</p>

47 <p>√(4/3) × 6 = (2√3)/3 × 6 = 4√3 ≈ 4.6188.</p>

49 <p>Well explained 👍</p>

48 <p>Well explained 👍</p>

50 <h3>Problem 4</h3>

49 <h3>Problem 4</h3>

51 <p>What will be the square root of (4/3 + 8/3)?</p>

50 <p>What will be the square root of (4/3 + 8/3)?</p>

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

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

53 <p>The square root is approximately 1.8257.</p>

52 <p>The square root is approximately 1.8257.</p>

54 <h3>Explanation</h3>

53 <h3>Explanation</h3>

55 <p>First, find the sum of (4/3 + 8/3) = 12/3 = 4.</p>

54 <p>First, find the sum of (4/3 + 8/3) = 12/3 = 4.</p>

56 <p>Then the square root of 4 is ±2.</p>

55 <p>Then the square root of 4 is ±2.</p>

57 <p>Therefore, the principal square root is 2.</p>

56 <p>Therefore, the principal square root is 2.</p>

58 <p>Well explained 👍</p>

57 <p>Well explained 👍</p>

59 <h3>Problem 5</h3>

58 <h3>Problem 5</h3>

60 <p>Find the perimeter of a rectangle if its length ‘l’ is √(4/3) units and the width ‘w’ is 2 units.</p>

59 <p>Find the perimeter of a rectangle if its length ‘l’ is √(4/3) units and the width ‘w’ is 2 units.</p>

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

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

62 <p>The perimeter of the rectangle is approximately 7.3333 units.</p>

61 <p>The perimeter of the rectangle is approximately 7.3333 units.</p>

63 <h3>Explanation</h3>

62 <h3>Explanation</h3>

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

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

65 <p>Perimeter = 2 × (√(4/3) + 2) = 2 × ((2√3)/3 + 2) ≈ 7.3333 units.</p>

64 <p>Perimeter = 2 × (√(4/3) + 2) = 2 × ((2√3)/3 + 2) ≈ 7.3333 units.</p>

66 <p>Well explained 👍</p>

65 <p>Well explained 👍</p>

67 <h2>FAQ on Square Root of 4/3</h2>

66 <h2>FAQ on Square Root of 4/3</h2>

68 <h3>1.What is √(4/3) in its simplest form?</h3>

67 <h3>1.What is √(4/3) in its simplest form?</h3>

69 <h3>2.What is the decimal approximation of √(4/3)?</h3>

68 <h3>2.What is the decimal approximation of √(4/3)?</h3>

70 <p>The<a>decimal</a>approximation of √(4/3) is approximately 1.1547.</p>

69 <p>The<a>decimal</a>approximation of √(4/3) is approximately 1.1547.</p>

71 <h3>3.Is 4/3 a perfect square?</h3>

70 <h3>3.Is 4/3 a perfect square?</h3>

72 <p>No, 4/3 is not a perfect square, as it does not result in an integer when its square root is taken.</p>

71 <p>No, 4/3 is not a perfect square, as it does not result in an integer when its square root is taken.</p>

73 <h3>4.Is √(4/3) rational or irrational?</h3>

72 <h3>4.Is √(4/3) rational or irrational?</h3>

74 <p>√(4/3) is an irrational number, as it cannot be expressed as a<a>ratio</a>of two integers.</p>

73 <p>√(4/3) is an irrational number, as it cannot be expressed as a<a>ratio</a>of two integers.</p>

75 <h3>5.What is the square of √(4/3)?</h3>

74 <h3>5.What is the square of √(4/3)?</h3>

76 <p>The square of √(4/3) is 4/3, as squaring a square root returns the original number.</p>

75 <p>The square of √(4/3) is 4/3, as squaring a square root returns the original number.</p>

77 <h2>Important Glossaries for the Square Root of 4/3</h2>

76 <h2>Important Glossaries for the Square Root of 4/3</h2>

78 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4 = 2², and the inverse of the square is the square root, √4 = 2.</li>

77 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4 = 2², and the inverse of the square is the square root, √4 = 2.</li>

79 </ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a ratio of two integers. For example, √3 is irrational.</li>

78 </ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a ratio of two integers. For example, √3 is irrational.</li>

80 </ul><ul><li><strong>Rationalization:</strong>The process of eliminating a radical from the denominator of a fraction.</li>

79 </ul><ul><li><strong>Rationalization:</strong>The process of eliminating a radical from the denominator of a fraction.</li>

81 </ul><ul><li><strong>Radical:</strong>An expression that uses the root symbol, such as √3, which denotes the square root of 3.</li>

80 </ul><ul><li><strong>Radical:</strong>An expression that uses the root symbol, such as √3, which denotes the square root of 3.</li>

82 </ul><ul><li><strong>Fraction:</strong>A numerical quantity that is not a whole number, represented by two numbers separated by a slash, like 4/3.</li>

81 </ul><ul><li><strong>Fraction:</strong>A numerical quantity that is not a whole number, represented by two numbers separated by a slash, like 4/3.</li>

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

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

84 <p>▶</p>

83 <p>▶</p>

85 <h2>Jaskaran Singh Saluja</h2>

84 <h2>Jaskaran Singh Saluja</h2>

86 <h3>About the Author</h3>

85 <h3>About the Author</h3>

87 <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>

86 <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>

88 <h3>Fun Fact</h3>

87 <h3>Fun Fact</h3>

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

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