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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 field of vehicle design, finance, etc. Here, we will discuss the square root of 15/4.</p>

4 <h2>What is the Square Root of 15/4?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. The<a>fraction</a>15/4 is not a<a>perfect square</a>. The square root of 15/4 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √(15/4), whereas (15/4)^(1/2) in the exponential form. √(15/4) = √15/2, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.</p>

6 <h2>Finding the Square Root of 15/4</h2>

7 <p>The<a>prime factorization</a>method is 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 15/4 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 15/4 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 15 and 4. Breaking them down, we get 15 = 3 × 5 and 4 = 2 × 2.</p>

14 <p><strong>Step 2:</strong>Now we found out the prime factors of 15 and 4. Since 15/4 is not a perfect square, we cannot pair the factors completely.</p>

15 <p>Therefore, calculating √(15/4) using prime factorization involves simplifying it to √15/2.</p>

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18 <h2>Square Root of 15/4 by Long Division Method</h2>

17 <h2>Square Root of 15/4 by Long Division Method</h2>

19 <p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square numbers for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>

18 <p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square numbers for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>

20 <p><strong>Step 1:</strong>To begin with, we'll find the square root of the<a>numerator</a>15 and the<a>denominator</a>4 separately.</p>

19 <p><strong>Step 1:</strong>To begin with, we'll find the square root of the<a>numerator</a>15 and the<a>denominator</a>4 separately.</p>

21 <p><strong>Step 2:</strong>The closest perfect square number to 15 is 16. The square root of 16 is 4, so √15 is slightly<a>less than</a>4.</p>

20 <p><strong>Step 2:</strong>The closest perfect square number to 15 is 16. The square root of 16 is 4, so √15 is slightly<a>less than</a>4.</p>

22 <p><strong>Step 3:</strong>For 4, the square root is 2.</p>

21 <p><strong>Step 3:</strong>For 4, the square root is 2.</p>

23 <p><strong>Step 4:</strong>Therefore, √(15/4) = √15/2. Using the long division method or a<a>calculator</a>, √15 ≈ 3.87298.</p>

22 <p><strong>Step 4:</strong>Therefore, √(15/4) = √15/2. Using the long division method or a<a>calculator</a>, √15 ≈ 3.87298.</p>

24 <h2>Square Root of 15/4 by Approximation Method</h2>

23 <h2>Square Root of 15/4 by Approximation Method</h2>

25 <p>The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 15/4 using the approximation method.</p>

24 <p>The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 15/4 using the approximation method.</p>

26 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares for the numerator 15, which are 9 and 16. √15 falls between 3 and 4.</p>

25 <p><strong>Step 1:</strong>Now we have to find the closest perfect squares for the numerator 15, which are 9 and 16. √15 falls between 3 and 4.</p>

27 <p><strong>Step 2:</strong>To approximate √15, we consider it as approximately 3.87298.</p>

26 <p><strong>Step 2:</strong>To approximate √15, we consider it as approximately 3.87298.</p>

28 <p><strong>Step 3:</strong>Therefore, √(15/4) is approximately 3.87298/2 = 1.93649.</p>

27 <p><strong>Step 3:</strong>Therefore, √(15/4) is approximately 3.87298/2 = 1.93649.</p>

29 <h2>Common Mistakes and How to Avoid Them in the Square Root of 15/4</h2>

28 <h2>Common Mistakes and How to Avoid Them in the Square Root of 15/4</h2>

30 <p>Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make in detail.</p>

29 <p>Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make in detail.</p>

31 <h3>Problem 1</h3>

30 <h3>Problem 1</h3>

32 <p>Can you help Max find the area of a square box if its side length is given as √(15/4)?</p>

31 <p>Can you help Max find the area of a square box if its side length is given as √(15/4)?</p>

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

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

34 <p>The area of the square is 15/4 square units.</p>

33 <p>The area of the square is 15/4 square units.</p>

35 <h3>Explanation</h3>

34 <h3>Explanation</h3>

36 <p>The area of the square = side².</p>

35 <p>The area of the square = side².</p>

37 <p>The side length is given as √(15/4).</p>

36 <p>The side length is given as √(15/4).</p>

38 <p>Area of the square = (√(15/4))²</p>

37 <p>Area of the square = (√(15/4))²</p>

39 <p>= 15/4.</p>

38 <p>= 15/4.</p>

40 <p>Therefore, the area of the square box is 15/4 square units.</p>

39 <p>Therefore, the area of the square box is 15/4 square units.</p>

41 <p>Well explained 👍</p>

40 <p>Well explained 👍</p>

42 <h3>Problem 2</h3>

41 <h3>Problem 2</h3>

43 <p>A square-shaped building measuring 15/4 square units is built; if each of the sides is √(15/4), what will be the square units of half of the building?</p>

42 <p>A square-shaped building measuring 15/4 square units is built; if each of the sides is √(15/4), what will be the square units of half of the building?</p>

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

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

45 <p>15/8 square units</p>

44 <p>15/8 square units</p>

46 <h3>Explanation</h3>

45 <h3>Explanation</h3>

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

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

48 <p>Dividing 15/4 by 2 = 15/8.</p>

47 <p>Dividing 15/4 by 2 = 15/8.</p>

49 <p>So half of the building measures 15/8 square units.</p>

48 <p>So half of the building measures 15/8 square units.</p>

50 <p>Well explained 👍</p>

49 <p>Well explained 👍</p>

51 <h3>Problem 3</h3>

50 <h3>Problem 3</h3>

52 <p>Calculate √(15/4) × 5.</p>

51 <p>Calculate √(15/4) × 5.</p>

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

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

54 <p>9.68245</p>

53 <p>9.68245</p>

55 <h3>Explanation</h3>

54 <h3>Explanation</h3>

56 <p>The first step is to find the approximate square root of 15/4, which is 1.93649.</p>

55 <p>The first step is to find the approximate square root of 15/4, which is 1.93649.</p>

57 <p>The second step is to multiply 1.93649 with 5.</p>

56 <p>The second step is to multiply 1.93649 with 5.</p>

58 <p>So 1.93649 × 5 ≈ 9.68245.</p>

57 <p>So 1.93649 × 5 ≈ 9.68245.</p>

59 <p>Well explained 👍</p>

58 <p>Well explained 👍</p>

60 <h3>Problem 4</h3>

59 <h3>Problem 4</h3>

61 <p>What will be the square root of (15/4 + 1)?</p>

60 <p>What will be the square root of (15/4 + 1)?</p>

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

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

63 <p>The square root is approximately 2.12132.</p>

62 <p>The square root is approximately 2.12132.</p>

64 <h3>Explanation</h3>

63 <h3>Explanation</h3>

65 <p>To find the square root, we need to find the sum of (15/4 + 1).</p>

64 <p>To find the square root, we need to find the sum of (15/4 + 1).</p>

66 <p>15/4 + 1 = 19/4, and then √(19/4) = √19/2 ≈ 2.12132.</p>

65 <p>15/4 + 1 = 19/4, and then √(19/4) = √19/2 ≈ 2.12132.</p>

67 <p>Therefore, the square root of (15/4 + 1) is approximately ±2.12132.</p>

66 <p>Therefore, the square root of (15/4 + 1) is approximately ±2.12132.</p>

68 <p>Well explained 👍</p>

67 <p>Well explained 👍</p>

69 <h3>Problem 5</h3>

68 <h3>Problem 5</h3>

70 <p>Find the perimeter of the rectangle if its length ‘l’ is √(15/4) units and the width ‘w’ is 2 units.</p>

69 <p>Find the perimeter of the rectangle if its length ‘l’ is √(15/4) units and the width ‘w’ is 2 units.</p>

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

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

72 <p>The perimeter of the rectangle is approximately 7.87298 units.</p>

71 <p>The perimeter of the rectangle is approximately 7.87298 units.</p>

73 <h3>Explanation</h3>

72 <h3>Explanation</h3>

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

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

75 <p>Perimeter = 2 × (√(15/4) + 2)</p>

74 <p>Perimeter = 2 × (√(15/4) + 2)</p>

76 <p>= 2 × (1.93649 + 2)</p>

75 <p>= 2 × (1.93649 + 2)</p>

77 <p>= 2 × 3.93649</p>

76 <p>= 2 × 3.93649</p>

78 <p>= 7.87298 units.</p>

77 <p>= 7.87298 units.</p>

79 <p>Well explained 👍</p>

78 <p>Well explained 👍</p>

80 <h2>FAQ on Square Root of 15/4</h2>

79 <h2>FAQ on Square Root of 15/4</h2>

81 <h3>1.What is √(15/4) in its simplest form?</h3>

80 <h3>1.What is √(15/4) in its simplest form?</h3>

82 <p>The prime factorization of 15 is 3 × 5, and 4 is 2 × 2, so the simplest form of √(15/4) = √15/2.</p>

81 <p>The prime factorization of 15 is 3 × 5, and 4 is 2 × 2, so the simplest form of √(15/4) = √15/2.</p>

83 <h3>2.Mention the factors of 15 and 4.</h3>

82 <h3>2.Mention the factors of 15 and 4.</h3>

84 <p>Factors of 15 are 1, 3, 5, and 15. Factors of 4 are 1, 2, and 4.</p>

83 <p>Factors of 15 are 1, 3, 5, and 15. Factors of 4 are 1, 2, and 4.</p>

85 <h3>3.Calculate the square of 15/4.</h3>

84 <h3>3.Calculate the square of 15/4.</h3>

86 <p>We get the square of 15/4 by multiplying the number by itself, that is (15/4) × (15/4) = 225/16.</p>

85 <p>We get the square of 15/4 by multiplying the number by itself, that is (15/4) × (15/4) = 225/16.</p>

87 <h3>4.Is 15/4 a prime fraction?</h3>

86 <h3>4.Is 15/4 a prime fraction?</h3>

88 <h3>5.15/4 is divisible by?</h3>

87 <h3>5.15/4 is divisible by?</h3>

89 <p>15/4 is divisible by 1, 3/4, 5/4, and 15/4.</p>

88 <p>15/4 is divisible by 1, 3/4, 5/4, and 15/4.</p>

90 <h2>Important Glossaries for the Square Root of 15/4</h2>

89 <h2>Important Glossaries for the Square Root of 15/4</h2>

91 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, that is, √16 = 4. </li>

90 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, that is, √16 = 4. </li>

92 <li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, q is not equal to zero, and p and q are integers. Example: √2 ≈ 1.414. </li>

91 <li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, q is not equal to zero, and p and q are integers. Example: √2 ≈ 1.414. </li>

93 <li><strong>Fraction:</strong>A fraction represents a part of a whole or, more generally, any number of equal parts. It is represented as p/q where p and q are integers and q ≠ 0. </li>

92 <li><strong>Fraction:</strong>A fraction represents a part of a whole or, more generally, any number of equal parts. It is represented as p/q where p and q are integers and q ≠ 0. </li>

94 <li><strong>Approximation:</strong>Approximating involves finding a value that is close enough to the right answer, usually within a specified range. </li>

93 <li><strong>Approximation:</strong>Approximating involves finding a value that is close enough to the right answer, usually within a specified range. </li>

95 <li><strong>Prime factorization:</strong>Prime factorization is the process of breaking down a number into its basic prime number components.</li>

94 <li><strong>Prime factorization:</strong>Prime factorization is the process of breaking down a number into its basic prime number components.</li>

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

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

97 <p>▶</p>

96 <p>▶</p>

98 <h2>Jaskaran Singh Saluja</h2>

97 <h2>Jaskaran Singh Saluja</h2>

99 <h3>About the Author</h3>

98 <h3>About the Author</h3>

100 <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>

99 <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>

101 <h3>Fun Fact</h3>

100 <h3>Fun Fact</h3>

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

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