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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 squaring a number is finding its square root. The square root has applications in various fields, such as vehicle design and finance. Here, we will discuss the square root of 5/4.</p>

4 <h2>What is the Square Root of 5/4?</h2>

5 <p>The<a>square</a>root is the inverse operation of squaring a<a>number</a>. The value 5/4 is not a<a>perfect square</a>. The square root of 5/4 can be expressed in both radical and exponential forms. In radical form, it is expressed as √(5/4), whereas in<a>exponential form</a>, it is expressed as (5/4)^(1/2). The square root of 5/4 is approximately 1.11803, which is an<a>irrational number</a>because it cannot be expressed as a<a>fraction</a>of<a>integers</a>.</p>

6 <h2>Finding the Square Root of 5/4</h2>

7 <p>The<a>prime factorization</a>method is typically used for perfect square numbers. However, for non-perfect squares like 5/4, we use methods such as the simplification of fractions, the long-<a>division</a>method, and approximation. Let us now explore these methods:</p>

8 <ul><li>Simplification of fractions</li>

9 <li>Long division method</li>

10 <li>Approximation method</li>

11 </ul><h2>Square Root of 5/4 by Simplification of Fractions</h2>

12 <p>To find the<a>square root</a>of a fraction, we take the square root of the<a>numerator</a>and the<a>denominator</a>separately.</p>

13 <p><strong>Step 1:</strong>The fraction is 5/4.</p>

14 <p><strong>Step 2:</strong>The square root of 5 is √5 and the square root of 4 is √4 = 2.</p>

15 <p><strong>Step 3:</strong>Therefore, the square root of 5/4 is √5/2.</p>

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18 <h2>Square Root of 5/4 by Long Division Method</h2>

17 <h2>Square Root of 5/4 by Long Division Method</h2>

19 <p>The<a>long division</a>method is used for finding more precise<a>decimal</a>values of square roots. Here’s how we can find the square root of 5/4 using this method:</p>

18 <p>The<a>long division</a>method is used for finding more precise<a>decimal</a>values of square roots. Here’s how we can find the square root of 5/4 using this method:</p>

20 <p><strong>Step 1:</strong>Convert the fraction 5/4 into a decimal, which is 1.25.</p>

19 <p><strong>Step 1:</strong>Convert the fraction 5/4 into a decimal, which is 1.25.</p>

21 <p><strong>Step 2:</strong>Group the numbers from the decimal point. In this case, we start with 1.25.</p>

20 <p><strong>Step 2:</strong>Group the numbers from the decimal point. In this case, we start with 1.25.</p>

22 <p><strong>Step 3:</strong>Find a number whose square is<a>less than</a>or equal to the first group (1.25). Here, 1 x 1 = 1 is less than 1.25.</p>

21 <p><strong>Step 3:</strong>Find a number whose square is<a>less than</a>or equal to the first group (1.25). Here, 1 x 1 = 1 is less than 1.25.</p>

23 <p><strong>Step 4:</strong>Subtract 1 from 1.25 to get 0.25, and bring down two zeros to make it 25.</p>

22 <p><strong>Step 4:</strong>Subtract 1 from 1.25 to get 0.25, and bring down two zeros to make it 25.</p>

24 <p><strong>Step 5:</strong>Double the<a>quotient</a>(1) and use it as the new<a>divisor</a>: 2x.</p>

23 <p><strong>Step 5:</strong>Double the<a>quotient</a>(1) and use it as the new<a>divisor</a>: 2x.</p>

25 <p><strong>Step 6:</strong>Find x such that 2x × x is less than or equal to 25. x is 1, as 21 × 1 = 21.</p>

24 <p><strong>Step 6:</strong>Find x such that 2x × x is less than or equal to 25. x is 1, as 21 × 1 = 21.</p>

26 <p><strong>Step 7:</strong>Subtract 21 from 25 to get 4, bring down more zeros, and continue the process to get more decimal places.</p>

25 <p><strong>Step 7:</strong>Subtract 21 from 25 to get 4, bring down more zeros, and continue the process to get more decimal places.</p>

27 <p>The square root of 1.25 is approximately 1.11803.</p>

26 <p>The square root of 1.25 is approximately 1.11803.</p>

28 <h2>Square Root of 5/4 by Approximation Method</h2>

27 <h2>Square Root of 5/4 by Approximation Method</h2>

29 <p>The approximation method provides a quick way to estimate square roots. Here’s how to find the square root of 5/4 using this method:</p>

28 <p>The approximation method provides a quick way to estimate square roots. Here’s how to find the square root of 5/4 using this method:</p>

30 <p><strong>Step 1:</strong>Identify the perfect squares near 1.25. The perfect squares closest to 1.25 are 1 (1^2) and 1.44 (1.2^2).</p>

29 <p><strong>Step 1:</strong>Identify the perfect squares near 1.25. The perfect squares closest to 1.25 are 1 (1^2) and 1.44 (1.2^2).</p>

31 <p><strong>Step 2:</strong>Since 1.25 is closer to 1.44, start with 1.1 as a rough estimate.</p>

30 <p><strong>Step 2:</strong>Since 1.25 is closer to 1.44, start with 1.1 as a rough estimate.</p>

32 <p><strong>Step 3:</strong>Calculate 1.1 × 1.1 = 1.21, which is less than 1.25. Step 4: Increase the estimate slightly to find a closer approximation, resulting in approximately 1.11803.</p>

31 <p><strong>Step 3:</strong>Calculate 1.1 × 1.1 = 1.21, which is less than 1.25. Step 4: Increase the estimate slightly to find a closer approximation, resulting in approximately 1.11803.</p>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 5/4</h2>

32 <h2>Common Mistakes and How to Avoid Them in the Square Root of 5/4</h2>

34 <p>Students make common mistakes when finding square roots, such as forgetting about negative square roots and misapplying methods. Let’s explore these mistakes in detail.</p>

33 <p>Students make common mistakes when finding square roots, such as forgetting about negative square roots and misapplying methods. Let’s explore these mistakes in detail.</p>

35 <h3>Problem 1</h3>

34 <h3>Problem 1</h3>

36 <p>Can you help Max find the area of a square with side length √(5/4)?</p>

35 <p>Can you help Max find the area of a square with side length √(5/4)?</p>

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

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

38 <p>The area of the square is approximately 1.25 square units.</p>

37 <p>The area of the square is approximately 1.25 square units.</p>

39 <h3>Explanation</h3>

38 <h3>Explanation</h3>

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

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

41 <p>The side length is given as √(5/4).</p>

40 <p>The side length is given as √(5/4).</p>

42 <p>Area of the square = (√(5/4))^2 = 5/4 = 1.25.</p>

41 <p>Area of the square = (√(5/4))^2 = 5/4 = 1.25.</p>

43 <p>Therefore, the area of the square is approximately 1.25 square units.</p>

42 <p>Therefore, the area of the square is approximately 1.25 square units.</p>

44 <p>Well explained 👍</p>

43 <p>Well explained 👍</p>

45 <h3>Problem 2</h3>

44 <h3>Problem 2</h3>

46 <p>A rectangle has a length of 5 units and a width of √(5/4) units. What is its area?</p>

45 <p>A rectangle has a length of 5 units and a width of √(5/4) units. What is its area?</p>

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

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

48 <p>The area of the rectangle is approximately 5.59015 square units.</p>

47 <p>The area of the rectangle is approximately 5.59015 square units.</p>

49 <h3>Explanation</h3>

48 <h3>Explanation</h3>

50 <p>Area = length × width = 5 × √(5/4).</p>

49 <p>Area = length × width = 5 × √(5/4).</p>

51 <p>First, calculate √(5/4) ≈ 1.11803.</p>

50 <p>First, calculate √(5/4) ≈ 1.11803.</p>

52 <p>Then, area = 5 × 1.11803 = 5.59015 square units.</p>

51 <p>Then, area = 5 × 1.11803 = 5.59015 square units.</p>

53 <p>Well explained 👍</p>

52 <p>Well explained 👍</p>

54 <h3>Problem 3</h3>

53 <h3>Problem 3</h3>

55 <p>Calculate √(5/4) × 8.</p>

54 <p>Calculate √(5/4) × 8.</p>

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

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

57 <p>Approximately 8.94424.</p>

56 <p>Approximately 8.94424.</p>

58 <h3>Explanation</h3>

57 <h3>Explanation</h3>

59 <p>Find the square root of 5/4, which is approximately 1.11803.</p>

58 <p>Find the square root of 5/4, which is approximately 1.11803.</p>

60 <p>Multiply 1.11803 by 8. 1.11803 × 8 ≈ 8.94424.</p>

59 <p>Multiply 1.11803 by 8. 1.11803 × 8 ≈ 8.94424.</p>

61 <p>Well explained 👍</p>

60 <p>Well explained 👍</p>

62 <h3>Problem 4</h3>

61 <h3>Problem 4</h3>

63 <p>What will be the square root of (5 + 4)?</p>

62 <p>What will be the square root of (5 + 4)?</p>

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

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

65 <p>The square root is 3.</p>

64 <p>The square root is 3.</p>

66 <h3>Explanation</h3>

65 <h3>Explanation</h3>

67 <p>Find the sum of (5 + 4) = 9. Then, √9 = 3. Therefore, the square root of (5 + 4) is ±3.</p>

66 <p>Find the sum of (5 + 4) = 9. Then, √9 = 3. Therefore, the square root of (5 + 4) is ±3.</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 a rectangle if its length ‘l’ is 5 units and the width ‘w’ is √(5/4) units.</p>

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

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

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

72 <p>The perimeter of the rectangle is approximately 12.23606 units.</p>

71 <p>The perimeter of the rectangle is approximately 12.23606 units.</p>

73 <h3>Explanation</h3>

72 <h3>Explanation</h3>

74 <p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (5 + √(5/4)) ≈ 2 × (5 + 1.11803) ≈ 2 × 6.11803 ≈ 12.23606 units.</p>

73 <p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (5 + √(5/4)) ≈ 2 × (5 + 1.11803) ≈ 2 × 6.11803 ≈ 12.23606 units.</p>

75 <p>Well explained 👍</p>

74 <p>Well explained 👍</p>

76 <h2>FAQ on Square Root of 5/4</h2>

75 <h2>FAQ on Square Root of 5/4</h2>

77 <h3>1.What is √(5/4) in its simplest form?</h3>

76 <h3>1.What is √(5/4) in its simplest form?</h3>

78 <p>The simplest form of √(5/4) is √5/2, which simplifies the square root of the numerator and the denominator separately.</p>

77 <p>The simplest form of √(5/4) is √5/2, which simplifies the square root of the numerator and the denominator separately.</p>

79 <h3>2.Mention the factors of 5/4.</h3>

78 <h3>2.Mention the factors of 5/4.</h3>

80 <p>The number 5/4 can be expressed as a fraction of integers, and its<a>factors</a>include 1, 5 (numerator), and 1, 2, and 4 (denominator).</p>

79 <p>The number 5/4 can be expressed as a fraction of integers, and its<a>factors</a>include 1, 5 (numerator), and 1, 2, and 4 (denominator).</p>

81 <h3>3.Calculate the square of 5/4.</h3>

80 <h3>3.Calculate the square of 5/4.</h3>

82 <p>The square of 5/4 is (5/4) × (5/4) = 25/16.</p>

81 <p>The square of 5/4 is (5/4) × (5/4) = 25/16.</p>

83 <h3>4.Is 5/4 a rational number?</h3>

82 <h3>4.Is 5/4 a rational number?</h3>

84 <p>Yes, 5/4 is a<a>rational number</a>because it can be expressed as a fraction of integers.</p>

83 <p>Yes, 5/4 is a<a>rational number</a>because it can be expressed as a fraction of integers.</p>

85 <h3>5.What is the decimal representation of 5/4?</h3>

84 <h3>5.What is the decimal representation of 5/4?</h3>

86 <h2>Important Glossaries for the Square Root of 5/4</h2>

85 <h2>Important Glossaries for the Square Root of 5/4</h2>

87 <ul><li><strong>Square root:</strong>The square root is the operation that finds a number which, when multiplied by itself, gives the original number. Example: The square root of 4 is 2, as 2 × 2 = 4.</li>

86 <ul><li><strong>Square root:</strong>The square root is the operation that finds a number which, when multiplied by itself, gives the original number. Example: The square root of 4 is 2, as 2 × 2 = 4.</li>

88 </ul><ul><li><strong>Rational number:</strong>A rational number can be expressed as a fraction of two integers, where the denominator is not zero.</li>

87 </ul><ul><li><strong>Rational number:</strong>A rational number can be expressed as a fraction of two integers, where the denominator is not zero.</li>

89 </ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction of two integers. Example: The square root of 2 is irrational.</li>

88 </ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction of two integers. Example: The square root of 2 is irrational.</li>

90 </ul><ul><li><strong>Fraction:</strong>A fraction represents a part of a whole and is expressed as a ratio of two numbers, the numerator and the denominator.</li>

89 </ul><ul><li><strong>Fraction:</strong>A fraction represents a part of a whole and is expressed as a ratio of two numbers, the numerator and the denominator.</li>

91 </ul><ul><li><strong>Decimal:</strong>A decimal is a number that has a whole number and a fractional part separated by a decimal point. Example: 1.25 is a decimal.</li>

90 </ul><ul><li><strong>Decimal:</strong>A decimal is a number that has a whole number and a fractional part separated by a decimal point. Example: 1.25 is a decimal.</li>

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

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

93 <p>▶</p>

92 <p>▶</p>

94 <h2>Jaskaran Singh Saluja</h2>

93 <h2>Jaskaran Singh Saluja</h2>

95 <h3>About the Author</h3>

94 <h3>About the Author</h3>

96 <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 <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>

97 <h3>Fun Fact</h3>

96 <h3>Fun Fact</h3>

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

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