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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 the square is a square root. The square root is used in fields such as engineering, mathematics, and physics. Here, we will discuss the square root of 16/3.</p>

4 <h2>What is the Square Root of 16/3?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 16/3 is not a<a>perfect square</a>. The square root of 16/3 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √(16/3), whereas (16/3)^(1/2) is the exponential form. √(16/3) = 2.3094, which is an<a>irrational number</a>because it cannot be expressed as a<a>fraction</a>p/q, where p and q are integers and q ≠ 0.</p>

6 <h2>Finding the Square Root of 16/3</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, we use methods like<a>long division</a>and approximation. Let us now learn the following methods:</p>

8 <ul><li>Long division method</li>

9 <li>Approximation method</li>

10 </ul><h2>Square Root of 16/3 by Long Division Method</h2>

11 <p>The long<a>division</a>method is particularly used for non-perfect square numbers. Here is how to find the<a>square root</a>of 16/3 using the long division method:</p>

12 <p><strong>Step 1:</strong>Convert the fraction 16/3 into a<a>decimal</a>. 16/3 = 5.3333...</p>

13 <p><strong>Step 2:</strong>Use the long division method to find the square root of 5.3333.</p>

14 <p><strong>Step 3:</strong>Estimate a number whose square is<a>less than</a>or equal to 5. Start with 2 because 2^2 = 4, which is less than 5.3333.</p>

15 <p><strong>Step 4:</strong>Bring down the next pair of digits after the decimal point. Divide 1.3333 by 4 to get 0.3333.</p>

16 <p><strong>Step 5:</strong>Continue the division to get more decimal places. The<a>quotient</a>becomes 2.3094 when rounded to four decimal places.</p>

17 <p>So, the square root of √(16/3) is approximately 2.3094.</p>

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20 <h2>Square Root of 16/3 by Approximation Method</h2>

19 <h2>Square Root of 16/3 by Approximation Method</h2>

21 <p>The approximation method is another way to find square roots. It is a simple method to estimate the square root of a given number. Now let us learn how to find the square root of 16/3 using the approximation method.</p>

20 <p>The approximation method is another way to find square roots. It is a simple method to estimate the square root of a given number. Now let us learn how to find the square root of 16/3 using the approximation method.</p>

22 <p><strong>Step 1:</strong>Estimate the value of √(5.3333) since 16/3 = 5.3333.</p>

21 <p><strong>Step 1:</strong>Estimate the value of √(5.3333) since 16/3 = 5.3333.</p>

23 <p><strong>Step 2:</strong>Find two numbers between which 5.3333 lies. It lies between 4 (2^2) and 9 (3^2).</p>

22 <p><strong>Step 2:</strong>Find two numbers between which 5.3333 lies. It lies between 4 (2^2) and 9 (3^2).</p>

24 <p><strong>Step 3:</strong>Use interpolation to approximate the value. Given number = 5.3333 Smallest perfect square = 4 Largest perfect square = 9 Using the<a>formula</a>: (5.3333 - 4) / (9 - 4) ≈ 0.2667</p>

23 <p><strong>Step 3:</strong>Use interpolation to approximate the value. Given number = 5.3333 Smallest perfect square = 4 Largest perfect square = 9 Using the<a>formula</a>: (5.3333 - 4) / (9 - 4) ≈ 0.2667</p>

25 <p><strong>Step 4:</strong>Add the decimal to the smaller root value: 2 + 0.2667 = 2.2667 So, the square root of 16/3 is approximately 2.2667.</p>

24 <p><strong>Step 4:</strong>Add the decimal to the smaller root value: 2 + 0.2667 = 2.2667 So, the square root of 16/3 is approximately 2.2667.</p>

26 <h2>Common Mistakes and How to Avoid Them in the Square Root of 16/3</h2>

25 <h2>Common Mistakes and How to Avoid Them in the Square Root of 16/3</h2>

27 <p>Students often make mistakes while finding the square root, such as ignoring the negative square root or skipping methods like long division. Let's look at a few common mistakes in detail.</p>

26 <p>Students often make mistakes while finding the square root, such as ignoring the negative square root or skipping methods like long division. Let's look at a few common 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 √(25/3)?</p>

28 <p>Can you help Max find the area of a square box if its side length is given as √(25/3)?</p>

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

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

31 <p>The area of the square is approximately 27.778 square units.</p>

30 <p>The area of the square is approximately 27.778 square units.</p>

32 <h3>Explanation</h3>

31 <h3>Explanation</h3>

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

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

34 <p>The side length is given as √(25/3).</p>

33 <p>The side length is given as √(25/3).</p>

35 <p>Area of the square = (√(25/3))^2 = 25/3 ≈ 8.333</p>

34 <p>Area of the square = (√(25/3))^2 = 25/3 ≈ 8.333</p>

36 <p>Therefore, the area of the square box is approximately 27.778 square units.</p>

35 <p>Therefore, the area of the square box is approximately 27.778 square units.</p>

37 <p>Well explained 👍</p>

36 <p>Well explained 👍</p>

38 <h3>Problem 2</h3>

37 <h3>Problem 2</h3>

39 <p>A square-shaped garden measures 16/3 square meters. If each of the sides is √(16/3), what will be the square meters of half of the garden?</p>

38 <p>A square-shaped garden measures 16/3 square meters. If each of the sides is √(16/3), what will be the square meters of half of the garden?</p>

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

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

41 <p>8/3 square meters.</p>

40 <p>8/3 square meters.</p>

42 <h3>Explanation</h3>

41 <h3>Explanation</h3>

43 <p>We divide the given area by 2 since the garden is square-shaped.</p>

42 <p>We divide the given area by 2 since the garden is square-shaped.</p>

44 <p>Dividing 16/3 by 2 gives us 8/3.</p>

43 <p>Dividing 16/3 by 2 gives us 8/3.</p>

45 <p>So, half of the garden measures 8/3 square meters.</p>

44 <p>So, half of the garden measures 8/3 square meters.</p>

46 <p>Well explained 👍</p>

45 <p>Well explained 👍</p>

47 <h3>Problem 3</h3>

46 <h3>Problem 3</h3>

48 <p>Calculate √(16/3) × 6.</p>

47 <p>Calculate √(16/3) × 6.</p>

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

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

50 <p>Approximately 13.8564.</p>

49 <p>Approximately 13.8564.</p>

51 <h3>Explanation</h3>

50 <h3>Explanation</h3>

52 <p>First, find the square root of 16/3, which is approximately 2.3094.</p>

51 <p>First, find the square root of 16/3, which is approximately 2.3094.</p>

53 <p>Then multiply 2.3094 by 6.</p>

52 <p>Then multiply 2.3094 by 6.</p>

54 <p>So, 2.3094 × 6 ≈ 13.8564.</p>

53 <p>So, 2.3094 × 6 ≈ 13.8564.</p>

55 <p>Well explained 👍</p>

54 <p>Well explained 👍</p>

56 <h3>Problem 4</h3>

55 <h3>Problem 4</h3>

57 <p>What will be the square root of (16/3 + 2/3)?</p>

56 <p>What will be the square root of (16/3 + 2/3)?</p>

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

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

59 <p>The square root is approximately 2.</p>

58 <p>The square root is approximately 2.</p>

60 <h3>Explanation</h3>

59 <h3>Explanation</h3>

61 <p>First, find the sum of (16/3 + 2/3). 16/3 + 2/3 = 18/3 = 6.</p>

60 <p>First, find the sum of (16/3 + 2/3). 16/3 + 2/3 = 18/3 = 6.</p>

62 <p>Then, find the square root of 6, which is approximately 2.4495.</p>

61 <p>Then, find the square root of 6, which is approximately 2.4495.</p>

63 <p>Therefore, the square root of (16/3 + 2/3) is approximately ±2.4495.</p>

62 <p>Therefore, the square root of (16/3 + 2/3) is approximately ±2.4495.</p>

64 <p>Well explained 👍</p>

63 <p>Well explained 👍</p>

65 <h3>Problem 5</h3>

64 <h3>Problem 5</h3>

66 <p>Find the perimeter of a rectangle if its length ‘l’ is √(16/3) units and the width ‘w’ is 5 units.</p>

65 <p>Find the perimeter of a rectangle if its length ‘l’ is √(16/3) units and the width ‘w’ is 5 units.</p>

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

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

68 <p>The perimeter of the rectangle is approximately 14.6188 units.</p>

67 <p>The perimeter of the rectangle is approximately 14.6188 units.</p>

69 <h3>Explanation</h3>

68 <h3>Explanation</h3>

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

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

71 <p>Perimeter = 2 × (√(16/3) + 5)</p>

70 <p>Perimeter = 2 × (√(16/3) + 5)</p>

72 <p>Perimeter = 2 × (2.3094 + 5) ≈ 14.6188 units.</p>

71 <p>Perimeter = 2 × (2.3094 + 5) ≈ 14.6188 units.</p>

73 <p>Well explained 👍</p>

72 <p>Well explained 👍</p>

74 <h2>FAQ on Square Root of 16/3</h2>

73 <h2>FAQ on Square Root of 16/3</h2>

75 <h3>1.What is √(16/3) in its simplest form?</h3>

74 <h3>1.What is √(16/3) in its simplest form?</h3>

76 <p>The simplest form of √(16/3) is √(16/3), which is approximately 2.3094.</p>

75 <p>The simplest form of √(16/3) is √(16/3), which is approximately 2.3094.</p>

77 <h3>2.Is 16/3 a perfect square?</h3>

76 <h3>2.Is 16/3 a perfect square?</h3>

78 <p>No, 16/3 is not a perfect square because it cannot be expressed as the square of an<a>integer</a>.</p>

77 <p>No, 16/3 is not a perfect square because it cannot be expressed as the square of an<a>integer</a>.</p>

79 <h3>3.Calculate the square of 16/3.</h3>

78 <h3>3.Calculate the square of 16/3.</h3>

80 <p>We get the square of 16/3 by multiplying the number by itself: (16/3) × (16/3) = 256/9 ≈ 28.4444.</p>

79 <p>We get the square of 16/3 by multiplying the number by itself: (16/3) × (16/3) = 256/9 ≈ 28.4444.</p>

81 <h3>4.Is 16/3 a rational number?</h3>

80 <h3>4.Is 16/3 a rational number?</h3>

82 <h3>5.16/3 is divisible by?</h3>

81 <h3>5.16/3 is divisible by?</h3>

83 <p>16/3 is a fraction and is not divisible in the conventional sense. To find divisibility, consider the<a>numerator</a>16, which is divisible by 1, 2, 4, 8, and 16.</p>

82 <p>16/3 is a fraction and is not divisible in the conventional sense. To find divisibility, consider the<a>numerator</a>16, which is divisible by 1, 2, 4, 8, and 16.</p>

84 <h2>Important Glossaries for the Square Root of 16/3</h2>

83 <h2>Important Glossaries for the Square Root of 16/3</h2>

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

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

86 </ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a ratio of two integers. For example, √2, which cannot be written as a simple fraction.</li>

85 </ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a ratio of two integers. For example, √2, which cannot be written as a simple fraction.</li>

87 </ul><ul><li><strong>Radical expression:</strong>A radical expression includes a root symbol, such as √x, where x is the radicand.</li>

86 </ul><ul><li><strong>Radical expression:</strong>A radical expression includes a root symbol, such as √x, where x is the radicand.</li>

88 </ul><ul><li><strong>Approximation:</strong>An approximation is an estimated value that is close to but not exactly equal to the true value.</li>

87 </ul><ul><li><strong>Approximation:</strong>An approximation is an estimated value that is close to but not exactly equal to the true value.</li>

89 </ul><ul><li><strong>Rational number:</strong>A rational number can be expressed as a fraction p/q, where p and q are integers and q ≠ 0.</li>

88 </ul><ul><li><strong>Rational number:</strong>A rational number can be expressed as a fraction p/q, where p and q are integers and q ≠ 0.</li>

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

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

91 <p>▶</p>

90 <p>▶</p>

92 <h2>Jaskaran Singh Saluja</h2>

91 <h2>Jaskaran Singh Saluja</h2>

93 <h3>About the Author</h3>

92 <h3>About the Author</h3>

94 <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>

93 <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>

95 <h3>Fun Fact</h3>

94 <h3>Fun Fact</h3>

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

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