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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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 9/4.</p>

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

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 9/4 is a<a>perfect square</a>. The square root of 9/4 is expressed in both radical and exponential forms. In the radical form, it is expressed as √(9/4), whereas (9/4)^(1/2) in the<a>exponential form</a>. √(9/4) = 3/2 = 1.5, 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 9/4</h2>

7 <h2>Square Root of 9/4 by Prime Factorization Method</h2>

8 <p>The<a>product</a>of<a>prime factors</a>is the prime factorization of a number. Now let us look at how 9/4 is broken down into its prime factors.</p>

9 <p><strong>Step 1:</strong>Finding the prime factors of 9 and 4 Breaking it down, 9 = 3 × 3 and 4 = 2 × 2.</p>

10 <p><strong>Step 2:</strong>Now we pair the prime factors. The square root of 9 is 3 (since 3 × 3 = 9) and the square root of 4 is 2 (since 2 × 2 = 4).</p>

11 <p>Therefore, calculating √(9/4) using prime factorization gives us 3/2.</p>

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14 <h2>Square Root of 9/4 by Long Division Method</h2>

13 <h2>Square Root of 9/4 by Long Division Method</h2>

15 <p>The<a>long division</a>method is particularly used for non-perfect square numbers, but it can also be applied to fractions. Let us learn how to find the square root using the long division method, step by step.</p>

14 <p>The<a>long division</a>method is particularly used for non-perfect square numbers, but it can also be applied to fractions. Let us learn how to find the square root using the long division method, step by step.</p>

16 <p><strong>Step 1:</strong>Consider the fraction 9/4. We can find the square root of the<a>numerator and denominator</a>separately.</p>

15 <p><strong>Step 1:</strong>Consider the fraction 9/4. We can find the square root of the<a>numerator and denominator</a>separately.</p>

17 <p><strong>Step 2:</strong>The square root of 9 is 3 and the square root of 4 is 2.</p>

16 <p><strong>Step 2:</strong>The square root of 9 is 3 and the square root of 4 is 2.</p>

18 <p><strong>Step 3:</strong>Therefore, the square root of 9/4 is 3/2.</p>

17 <p><strong>Step 3:</strong>Therefore, the square root of 9/4 is 3/2.</p>

19 <h2>Square Root of 9/4 by Approximation Method</h2>

18 <h2>Square Root of 9/4 by Approximation Method</h2>

20 <p>Approximation method is another method for finding square roots, especially useful for non-perfect squares, but not needed here as 9/4 is a perfect square. However, let us briefly consider this method.</p>

19 <p>Approximation method is another method for finding square roots, especially useful for non-perfect squares, but not needed here as 9/4 is a perfect square. However, let us briefly consider this method.</p>

21 <p><strong>Step 1:</strong>Identify the closest perfect squares to 9 and 4, which are 9 and 4 themselves.</p>

20 <p><strong>Step 1:</strong>Identify the closest perfect squares to 9 and 4, which are 9 and 4 themselves.</p>

22 <p><strong>Step 2:</strong>Since both the numerator and the denominator are perfect squares, the square root of 9/4 is exactly 3/2 or 1.5 without needing approximation.</p>

21 <p><strong>Step 2:</strong>Since both the numerator and the denominator are perfect squares, the square root of 9/4 is exactly 3/2 or 1.5 without needing approximation.</p>

23 <h2>Common Mistakes and How to Avoid Them in the Square Root of 9/4</h2>

22 <h2>Common Mistakes and How to Avoid Them in the Square Root of 9/4</h2>

24 <p>Students may make mistakes while finding the square root, such as forgetting about the negative square root or incorrectly simplifying fractions. Let's look at a few common errors in detail.</p>

23 <p>Students may make mistakes while finding the square root, such as forgetting about the negative square root or incorrectly simplifying fractions. Let's look at a few common errors 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 √(9/4)?</p>

25 <p>Can you help Max find the area of a square box if its side length is given as √(9/4)?</p>

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

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

28 <p>The area of the square is 2.25 square units.</p>

27 <p>The area of the square is 2.25 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 √(9/4).</p>

30 <p>The side length is given as √(9/4).</p>

32 <p>Area of the square = (√(9/4))^2 = (3/2)^2 = 2.25.</p>

31 <p>Area of the square = (√(9/4))^2 = (3/2)^2 = 2.25.</p>

33 <p>Therefore, the area of the square box is 2.25 square units.</p>

32 <p>Therefore, the area of the square box is 2.25 square units.</p>

34 <p>Well explained 👍</p>

33 <p>Well explained 👍</p>

35 <h3>Problem 2</h3>

34 <h3>Problem 2</h3>

36 <p>A square-shaped building measuring 9/4 square meters is built; if each of the sides is √(9/4), what will be the square meters of half of the building?</p>

35 <p>A square-shaped building measuring 9/4 square meters is built; if each of the sides is √(9/4), what will be the square meters of half of the building?</p>

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

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

38 <p>1.125 square meters</p>

37 <p>1.125 square meters</p>

39 <h3>Explanation</h3>

38 <h3>Explanation</h3>

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

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

41 <p>Dividing 9/4 by 2 gives us 1.125.</p>

40 <p>Dividing 9/4 by 2 gives us 1.125.</p>

42 <p>So half of the building measures 1.125 square meters.</p>

41 <p>So half of the building measures 1.125 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 √(9/4) × 5.</p>

44 <p>Calculate √(9/4) × 5.</p>

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

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

47 <p>7.5</p>

46 <p>7.5</p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>The first step is to find the square root of 9/4, which is 3/2 or 1.5.</p>

48 <p>The first step is to find the square root of 9/4, which is 3/2 or 1.5.</p>

50 <p>The second step is to multiply 1.5 by 5.</p>

49 <p>The second step is to multiply 1.5 by 5.</p>

51 <p>So 1.5 × 5 = 7.5.</p>

50 <p>So 1.5 × 5 = 7.5.</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 (9 + 1)?</p>

53 <p>What will be the square root of (9 + 1)?</p>

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

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

56 <p>The square root is 3.162</p>

55 <p>The square root is 3.162</p>

57 <h3>Explanation</h3>

56 <h3>Explanation</h3>

58 <p>To find the square root, we need to find the sum of (9 + 1).</p>

57 <p>To find the square root, we need to find the sum of (9 + 1).</p>

59 <p>9 + 1 = 10, and then √10 ≈ 3.162.</p>

58 <p>9 + 1 = 10, and then √10 ≈ 3.162.</p>

60 <p>Therefore, the square root of (9 + 1) is approximately ±3.162.</p>

59 <p>Therefore, the square root of (9 + 1) is approximately ±3.162.</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 a rectangle if its length ‘l’ is √(9/4) units and the width ‘w’ is 5 units.</p>

62 <p>Find the perimeter of a rectangle if its length ‘l’ is √(9/4) units and the width ‘w’ is 5 units.</p>

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

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

65 <p>The perimeter of the rectangle is 13 units.</p>

64 <p>The perimeter of the rectangle is 13 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 × (√(9/4) + 5) = 2 × (1.5 + 5) = 2 × 6.5 = 13 units.</p>

67 <p>Perimeter = 2 × (√(9/4) + 5) = 2 × (1.5 + 5) = 2 × 6.5 = 13 units.</p>

69 <p>Well explained 👍</p>

68 <p>Well explained 👍</p>

70 <h2>FAQ on Square Root of 9/4</h2>

69 <h2>FAQ on Square Root of 9/4</h2>

71 <h3>1.What is √(9/4) in its simplest form?</h3>

70 <h3>1.What is √(9/4) in its simplest form?</h3>

72 <p>The prime factorization of 9 is 3 × 3 and of 4 is 2 × 2. The simplest form of √(9/4) is 3/2 or 1.5.</p>

71 <p>The prime factorization of 9 is 3 × 3 and of 4 is 2 × 2. The simplest form of √(9/4) is 3/2 or 1.5.</p>

73 <h3>2.Is 9/4 a perfect square?</h3>

72 <h3>2.Is 9/4 a perfect square?</h3>

74 <p>Yes, 9/4 is a perfect square because both 9 and 4 are perfect squares.</p>

73 <p>Yes, 9/4 is a perfect square because both 9 and 4 are perfect squares.</p>

75 <h3>3.Calculate the square of 9/4.</h3>

74 <h3>3.Calculate the square of 9/4.</h3>

76 <p>We get the square of 9/4 by multiplying the number by itself, that is (9/4) × (9/4) = 81/16.</p>

75 <p>We get the square of 9/4 by multiplying the number by itself, that is (9/4) × (9/4) = 81/16.</p>

77 <h3>4.Is 9/4 a rational number?</h3>

76 <h3>4.Is 9/4 a rational number?</h3>

78 <p>Yes, 9/4 is a rational number because it can be expressed as a fraction of two integers.</p>

77 <p>Yes, 9/4 is a rational number because it can be expressed as a fraction of two integers.</p>

79 <h3>5.What is the decimal form of 9/4?</h3>

78 <h3>5.What is the decimal form of 9/4?</h3>

80 <h2>Important Glossaries for the Square Root of 9/4</h2>

79 <h2>Important Glossaries for the Square Root of 9/4</h2>

81 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 3^2 = 9 and the inverse of the square is the square root, which is √9 = 3.</li>

80 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 3^2 = 9 and the inverse of the square is the square root, which is √9 = 3.</li>

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

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

83 </ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that can be expressed as the square of an integer or a fraction. Example: 9/4 is a perfect square because it equals (3/2)^2.</li>

82 </ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that can be expressed as the square of an integer or a fraction. Example: 9/4 is a perfect square because it equals (3/2)^2.</li>

84 </ul><ul><li><strong>Fraction:</strong>A fraction represents a part of a whole and is expressed as a numerator divided by a denominator, such as 9/4.</li>

83 </ul><ul><li><strong>Fraction:</strong>A fraction represents a part of a whole and is expressed as a numerator divided by a denominator, such as 9/4.</li>

85 </ul><ul><li><strong>Numerator and Denominator:</strong>In a fraction, the numerator is the top number and the denominator is the bottom number. They represent how many parts of a whole are being considered.</li>

84 </ul><ul><li><strong>Numerator and Denominator:</strong>In a fraction, the numerator is the top number and the denominator is the bottom number. They represent how many parts of a whole are being considered.</li>

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

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

87 <p>▶</p>

86 <p>▶</p>

88 <h2>Jaskaran Singh Saluja</h2>

87 <h2>Jaskaran Singh Saluja</h2>

89 <h3>About the Author</h3>

88 <h3>About the Author</h3>

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>

89 <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>

91 <h3>Fun Fact</h3>

90 <h3>Fun Fact</h3>

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

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