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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 fields of vehicle design, finance, etc. Here, we will discuss the square root of 16/9.</p>

4 <h2>What is the Square Root of 16/9?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 16/9 is a<a>perfect square</a>. The square root of 16/9 is expressed in both radical and fractional form. In the radical form, it is expressed as, √(16/9), whereas in fractional form, it can be simplified to (4/3). The square root of 16/9 is 4/3, which is a<a>rational number</a>because it can 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 16/9</h2>

7 <p>The<a>prime factorization</a>method can be used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 16/9 by Prime Factorization Method</h2>

12 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 16/9 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 16 and 9 Breaking it down, we get 16 = 2 × 2 × 2 × 2 and 9 = 3 × 3.</p>

14 <p><strong>Step 2:</strong>Now we found out the prime factors of 16 and 9. We pair the prime factors: (2 × 2) and (3).</p>

15 <p><strong>Step 3:</strong>Since both 16 and 9 are perfect squares, we can find their square roots easily: √16 = 4 and √9 = 3.</p>

16 <p>Therefore, the<a>square root</a>of 16/9 using prime factorization is 4/3.</p>

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19 <h2>Square Root of 16/9 by Long Division Method</h2>

18 <h2>Square Root of 16/9 by Long Division Method</h2>

20 <p>The<a>long division</a>method is particularly used for non-perfect square numbers. However, 16/9 is a perfect square, so the long division method is not necessary here. We can directly find the square root by simplifying the<a>fraction</a>to 4/3.</p>

19 <p>The<a>long division</a>method is particularly used for non-perfect square numbers. However, 16/9 is a perfect square, so the long division method is not necessary here. We can directly find the square root by simplifying the<a>fraction</a>to 4/3.</p>

21 <h2>Square Root of 16/9 by Approximation Method</h2>

20 <h2>Square Root of 16/9 by Approximation Method</h2>

22 <p>The approximation method is another method for finding the square roots. It is an easy method to find the square root of a given number. However, since 16/9 is a perfect square, approximation is not needed. The exact square root is 4/3.</p>

21 <p>The approximation method is another method for finding the square roots. It is an easy method to find the square root of a given number. However, since 16/9 is a perfect square, approximation is not needed. The exact square root is 4/3.</p>

23 <h2>Common Mistakes and How to Avoid Them in the Square Root of 16/9</h2>

22 <h2>Common Mistakes and How to Avoid Them in the Square Root of 16/9</h2>

24 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root. Skipping steps in the long division method, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>

23 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root. Skipping steps in the long division method, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>

25 <h3>Problem 1</h3>

24 <h3>Problem 1</h3>

26 <p>Can you help Max find the area of a square box if its side length is given as √(25/16)?</p>

25 <p>Can you help Max find the area of a square box if its side length is given as √(25/16)?</p>

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

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

28 <p>The area of the square is 25/16 square units.</p>

27 <p>The area of the square is 25/16 square units.</p>

29 <h3>Explanation</h3>

28 <h3>Explanation</h3>

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

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

31 <p>The side length is given as √(25/16).</p>

30 <p>The side length is given as √(25/16).</p>

32 <p>Area of the square = side^2</p>

31 <p>Area of the square = side^2</p>

33 <p>= (5/4) × (5/4)</p>

32 <p>= (5/4) × (5/4)</p>

34 <p>= 25/16.</p>

33 <p>= 25/16.</p>

35 <p>Therefore, the area of the square box is 25/16 square units.</p>

34 <p>Therefore, the area of the square box is 25/16 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 field measures 16/9 square meters; if each of the sides is √(16/9), what will be the square meters of half of the field?</p>

37 <p>A square-shaped field measures 16/9 square meters; if each of the sides is √(16/9), what will be the square meters of half of the field?</p>

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

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

40 <p>8/9 square meters</p>

39 <p>8/9 square meters</p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>We can just divide the given area by 2 as the field is square-shaped. Dividing 16/9 by 2, we get 8/9. So half of the field measures 8/9 square meters.</p>

41 <p>We can just divide the given area by 2 as the field is square-shaped. Dividing 16/9 by 2, we get 8/9. So half of the field measures 8/9 square 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 √(16/9) × 5.</p>

44 <p>Calculate √(16/9) × 5.</p>

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

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

47 <p>20/3</p>

46 <p>20/3</p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>The first step is to find the square root of 16/9, which is 4/3.</p>

48 <p>The first step is to find the square root of 16/9, which is 4/3.</p>

50 <p>The second step is to multiply 4/3 by 5.</p>

49 <p>The second step is to multiply 4/3 by 5.</p>

51 <p>So (4/3) × 5 = 20/3.</p>

50 <p>So (4/3) × 5 = 20/3.</p>

52 <p>Well explained 👍</p>

51 <p>Well explained 👍</p>

53 <h3>Problem 4</h3>

52 <h3>Problem 4</h3>

54 <p>What will be the square root of (25/9 + 4/9)?</p>

53 <p>What will be the square root of (25/9 + 4/9)?</p>

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

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

56 <p>The square root is 3/2.</p>

55 <p>The square root is 3/2.</p>

57 <h3>Explanation</h3>

56 <h3>Explanation</h3>

58 <p>To find the square root, we need to find the sum of (25/9 + 4/9).</p>

57 <p>To find the square root, we need to find the sum of (25/9 + 4/9).</p>

59 <p>25/9 + 4/9 = 29/9, and then the square root of 29/9 is approximately 3/2.</p>

58 <p>25/9 + 4/9 = 29/9, and then the square root of 29/9 is approximately 3/2.</p>

60 <p>Therefore, the square root of (25/9 + 4/9) is ±3/2.</p>

59 <p>Therefore, the square root of (25/9 + 4/9) is ±3/2.</p>

61 <p>Well explained 👍</p>

60 <p>Well explained 👍</p>

62 <h3>Problem 5</h3>

61 <h3>Problem 5</h3>

63 <p>Find the perimeter of the rectangle if its length ‘l’ is √(25/16) units and the width ‘w’ is 6 units.</p>

62 <p>Find the perimeter of the rectangle if its length ‘l’ is √(25/16) units and the width ‘w’ is 6 units.</p>

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

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

65 <p>We find the perimeter of the rectangle as 14.5 units.</p>

64 <p>We find the perimeter of the rectangle as 14.5 units.</p>

66 <h3>Explanation</h3>

65 <h3>Explanation</h3>

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

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

68 <p>Perimeter = 2 × (√(25/16) + 6)</p>

67 <p>Perimeter = 2 × (√(25/16) + 6)</p>

69 <p>= 2 × (5/4 + 6)</p>

68 <p>= 2 × (5/4 + 6)</p>

70 <p>= 2 × (29/4)</p>

69 <p>= 2 × (29/4)</p>

71 <p>= 14.5 units.</p>

70 <p>= 14.5 units.</p>

72 <p>Well explained 👍</p>

71 <p>Well explained 👍</p>

73 <h2>FAQ on Square Root of 16/9</h2>

72 <h2>FAQ on Square Root of 16/9</h2>

74 <h3>1.What is √(16/9) in its simplest form?</h3>

73 <h3>1.What is √(16/9) in its simplest form?</h3>

75 <p>The prime factorization of 16 is 2 × 2 × 2 × 2 and 9 is 3 × 3, so the simplest form of √(16/9) is 4/3.</p>

74 <p>The prime factorization of 16 is 2 × 2 × 2 × 2 and 9 is 3 × 3, so the simplest form of √(16/9) is 4/3.</p>

76 <h3>2.Mention the factors of 16 and 9.</h3>

75 <h3>2.Mention the factors of 16 and 9.</h3>

77 <p>Factors of 16 are 1, 2, 4, 8, and 16, while factors of 9 are 1, 3, and 9.</p>

76 <p>Factors of 16 are 1, 2, 4, 8, and 16, while factors of 9 are 1, 3, and 9.</p>

78 <h3>3.Calculate the square of 16/9.</h3>

77 <h3>3.Calculate the square of 16/9.</h3>

79 <p>We get the square of 16/9 by multiplying the number by itself, that is (16/9) × (16/9) = 256/81.</p>

78 <p>We get the square of 16/9 by multiplying the number by itself, that is (16/9) × (16/9) = 256/81.</p>

80 <h3>4.Is 16/9 a prime number?</h3>

79 <h3>4.Is 16/9 a prime number?</h3>

81 <h3>5.16/9 is divisible by?</h3>

80 <h3>5.16/9 is divisible by?</h3>

82 <p>16 and 9 have their own factors, but as a fraction, 16/9 is not divisible by any whole number except for 1.</p>

81 <p>16 and 9 have their own factors, but as a fraction, 16/9 is not divisible by any whole number except for 1.</p>

83 <h2>Important Glossaries for the Square Root of 16/9</h2>

82 <h2>Important Glossaries for the Square Root of 16/9</h2>

84 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: (4/3)^2 = 16/9 and the inverse of the square is the square root, that is √(16/9) = 4/3. </li>

83 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: (4/3)^2 = 16/9 and the inverse of the square is the square root, that is √(16/9) = 4/3. </li>

85 <li><strong>Rational number:</strong>A rational number is a number that can be written in the form of p/q, q is not equal to zero, and p and q are integers. </li>

84 <li><strong>Rational number:</strong>A rational number is a number that can be written in the form of p/q, q is not equal to zero, and p and q are integers. </li>

86 <li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root. </li>

85 <li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root. </li>

87 <li><strong>Fraction:</strong>A fraction represents a part of a whole or, more generally, any number of equal parts. It consists of a numerator and a denominator. </li>

86 <li><strong>Fraction:</strong>A fraction represents a part of a whole or, more generally, any number of equal parts. It consists of a numerator and a denominator. </li>

88 <li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer or a fraction. For example, 16/9 is a perfect square because its square root is 4/3.</li>

87 <li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer or a fraction. For example, 16/9 is a perfect square because its square root is 4/3.</li>

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

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

90 <p>▶</p>

89 <p>▶</p>

91 <h2>Jaskaran Singh Saluja</h2>

90 <h2>Jaskaran Singh Saluja</h2>

92 <h3>About the Author</h3>

91 <h3>About the Author</h3>

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>

92 <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>

94 <h3>Fun Fact</h3>

93 <h3>Fun Fact</h3>

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

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