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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 vehicle design, finance, etc. Here, we will discuss the square root of 8/3.</p>

4 <h2>What is the Square Root of 8/3?</h2>

5 <p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 8/3 is not a<a>perfect square</a>. The square root of 8/3 can be expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √(8/3), whereas in exponential form, it is (8/3)^(1/2). The square root of 8/3 is approximately 1.63299, 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 8/3</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, methods such as 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 8/3 by Long Division Method</h2>

12 <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>of 8/3 using the long division method, step by step:</p>

13 <p><strong>Step 1:</strong>Convert the<a>fraction</a>8/3 to a<a>decimal</a>, which is approximately 2.6667.</p>

14 <p><strong>Step 2:</strong>Group the digits from left to right.</p>

15 <p><strong>Step 3:</strong>Find a number whose square is<a>less than</a>or equal to 2.66. Begin with 1 since 1 x 1 = 1.</p>

16 <p><strong>Step 4:</strong>Subtract 1 from 2.66, bringing down the next pair of digits.</p>

17 <p><strong>Step 5:</strong>Double the current<a>quotient</a>and find a suitable digit to append to it, which when multiplied by itself, gives a<a>product</a>less than or equal to the current dividend. Repeat these steps until the desired accuracy is achieved.</p>

18 <p>The square root of 8/3 is approximately 1.63299.</p>

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21 <h2>Square Root of 8/3 by Approximation Method</h2>

20 <h2>Square Root of 8/3 by Approximation Method</h2>

22 <p>The approximation method is another way to find square roots. It is an easy method for estimating the square root of a given number. Here's how to find the square root of 8/3 using the approximation method:</p>

21 <p>The approximation method is another way to find square roots. It is an easy method for estimating the square root of a given number. Here's how to find the square root of 8/3 using the approximation method:</p>

23 <p><strong>Step 1:</strong>Approximate the fraction 8/3 as the decimal 2.6667.</p>

22 <p><strong>Step 1:</strong>Approximate the fraction 8/3 as the decimal 2.6667.</p>

24 <p><strong>Step 2:</strong>Identify the closest perfect squares around 2.6667. The perfect squares 1 (1^2) and 4 (2^2) bracket 2.6667.</p>

23 <p><strong>Step 2:</strong>Identify the closest perfect squares around 2.6667. The perfect squares 1 (1^2) and 4 (2^2) bracket 2.6667.</p>

25 <p><strong>Step 3:</strong>Use interpolation to estimate between these two values. The linear approximation will give you a result close to 1.63299.</p>

24 <p><strong>Step 3:</strong>Use interpolation to estimate between these two values. The linear approximation will give you a result close to 1.63299.</p>

26 <h2>Common Mistakes and How to Avoid Them in Finding the Square Root of 8/3</h2>

25 <h2>Common Mistakes and How to Avoid Them in Finding the Square Root of 8/3</h2>

27 <p>Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping long division steps, etc. Let us look at a few of these mistakes in detail.</p>

26 <p>Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping long division steps, etc. Let us look at a few of these mistakes in detail.</p>

28 <h3>Problem 1</h3>

27 <h3>Problem 1</h3>

29 <p>Can you help Max find the area of a square box if its side length is given as √(8/3)?</p>

28 <p>Can you help Max find the area of a square box if its side length is given as √(8/3)?</p>

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

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

31 <p>The area of the square is approximately 2.667 square units.</p>

30 <p>The area of the square is approximately 2.667 square units.</p>

32 <h3>Explanation</h3>

31 <h3>Explanation</h3>

33 <p>The area of a square = side^2.</p>

32 <p>The area of a square = side^2.</p>

34 <p>If the side length is √(8/3), then the area = (√(8/3))^2 = 8/3 ≈ 2.667 square units.</p>

33 <p>If the side length is √(8/3), then the area = (√(8/3))^2 = 8/3 ≈ 2.667 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 garden covers an area of 8/3 square meters. What is the length of each side of the garden?</p>

36 <p>A square-shaped garden covers an area of 8/3 square meters. What is the length of each side of the garden?</p>

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

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

39 <p>The length of each side is approximately 1.633 meters.</p>

38 <p>The length of each side is approximately 1.633 meters.</p>

40 <h3>Explanation</h3>

39 <h3>Explanation</h3>

41 <p>The side length of a square is the square root of its area.</p>

40 <p>The side length of a square is the square root of its area.</p>

42 <p>Thus, the side length is √(8/3) ≈ 1.633 meters.</p>

41 <p>Thus, the side length is √(8/3) ≈ 1.633 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 √(8/3) x 5.</p>

44 <p>Calculate √(8/3) x 5.</p>

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

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

47 <p>Approximately 8.165.</p>

46 <p>Approximately 8.165.</p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>First, find the square root of 8/3, which is approximately 1.633, then multiply by 5: 1.633 x 5 ≈ 8.165.</p>

48 <p>First, find the square root of 8/3, which is approximately 1.633, then multiply by 5: 1.633 x 5 ≈ 8.165.</p>

50 <p>Well explained 👍</p>

49 <p>Well explained 👍</p>

51 <h3>Problem 4</h3>

50 <h3>Problem 4</h3>

52 <p>What will be the square root of (8/3 + 1)?</p>

51 <p>What will be the square root of (8/3 + 1)?</p>

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

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

54 <p>Approximately 1.915.</p>

53 <p>Approximately 1.915.</p>

55 <h3>Explanation</h3>

54 <h3>Explanation</h3>

56 <p>First, compute 8/3 + 1 = 11/3.</p>

55 <p>First, compute 8/3 + 1 = 11/3.</p>

57 <p>Then, find √(11/3) ≈ 1.915.</p>

56 <p>Then, find √(11/3) ≈ 1.915.</p>

58 <p>Well explained 👍</p>

57 <p>Well explained 👍</p>

59 <h2>FAQ on Square Root of 8/3</h2>

58 <h2>FAQ on Square Root of 8/3</h2>

60 <h3>1.What is √(8/3) in its simplest form?</h3>

59 <h3>1.What is √(8/3) in its simplest form?</h3>

61 <p>The simplest radical form of √(8/3) is √8/√3, which can be simplified further using<a>rationalization</a>techniques.</p>

60 <p>The simplest radical form of √(8/3) is √8/√3, which can be simplified further using<a>rationalization</a>techniques.</p>

62 <h3>2.Is 8/3 a perfect square?</h3>

61 <h3>2.Is 8/3 a perfect square?</h3>

63 <p>No, 8/3 is not a perfect square as it cannot be expressed as the square of an integer.</p>

62 <p>No, 8/3 is not a perfect square as it cannot be expressed as the square of an integer.</p>

64 <h3>3.How do you calculate the square of 8/3?</h3>

63 <h3>3.How do you calculate the square of 8/3?</h3>

65 <p>The square of 8/3 is (8/3) x (8/3) = 64/9.</p>

64 <p>The square of 8/3 is (8/3) x (8/3) = 64/9.</p>

66 <h3>4.Is 8/3 greater than 2?</h3>

65 <h3>4.Is 8/3 greater than 2?</h3>

67 <h3>5.What is the decimal approximation of √(8/3)?</h3>

66 <h3>5.What is the decimal approximation of √(8/3)?</h3>

68 <p>The decimal approximation of √(8/3) is approximately 1.63299.</p>

67 <p>The decimal approximation of √(8/3) is approximately 1.63299.</p>

69 <h2>Important Glossary for the Square Root of 8/3</h2>

68 <h2>Important Glossary for the Square Root of 8/3</h2>

70 <ul><li><strong>Square root:</strong>The square root is the inverse operation of squaring a number. For example, 4^2 = 16, so √16 = 4.</li>

69 <ul><li><strong>Square root:</strong>The square root is the inverse operation of squaring a number. For example, 4^2 = 16, so √16 = 4.</li>

71 </ul><ul><li><strong>Irrational number:</strong>A number that cannot be expressed as a simple fraction, such as √2 or √(8/3).</li>

70 </ul><ul><li><strong>Irrational number:</strong>A number that cannot be expressed as a simple fraction, such as √2 or √(8/3).</li>

72 </ul><ul><li><strong>Decimal:</strong>A fractional number expressed in<a>base</a>10, such as 1.63299.</li>

71 </ul><ul><li><strong>Decimal:</strong>A fractional number expressed in<a>base</a>10, such as 1.63299.</li>

73 </ul><ul><li><strong>Radical:</strong>An<a>expression</a>that uses the root symbol (√) to denote roots, such as √8.</li>

72 </ul><ul><li><strong>Radical:</strong>An<a>expression</a>that uses the root symbol (√) to denote roots, such as √8.</li>

74 </ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer, such as 4 (2^2) or 9 (3^2).</li>

73 </ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer, such as 4 (2^2) or 9 (3^2).</li>

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

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

76 <p>▶</p>

75 <p>▶</p>

77 <h2>Jaskaran Singh Saluja</h2>

76 <h2>Jaskaran Singh Saluja</h2>

78 <h3>About the Author</h3>

77 <h3>About the Author</h3>

79 <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>

78 <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>

80 <h3>Fun Fact</h3>

79 <h3>Fun Fact</h3>

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

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