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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 various fields like vehicle design, finance, etc. Here, we will discuss the square root of 3/4.</p>

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

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 3/4 is not a<a>perfect square</a>. The square root of 3/4 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √(3/4), whereas (3/4)^(1/2) in exponential form. √(3/4) = √3/2, which is an<a>irrational number</a>because it cannot 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 3/4</h2>

7 <p>Since 3/4 is a<a>fraction</a>, we use the property of square roots that allows us to take the<a>square root</a>of the<a>numerator</a>and the<a>denominator</a>separately. Let us now learn the following methods:</p>

8 <ul><li>Prime factorization method</li>

9 <li>Simplification method</li>

10 <li>Numerical approximation method</li>

11 </ul><h2>Square Root of 3/4 by Simplification Method</h2>

12 <p>The simplification method allows us to find the square root of a fraction by taking the square root of the numerator and the denominator separately. Step 1: The numerator is 3, and the denominator is 4. Step 2: Take the square root of each part separately: √3 and √4. Step 3: The square root of 4 is 2, as 2 x 2 = 4. Step 4: Therefore, the square root of 3/4 is √3/2.</p>

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15 <h2>Square Root of 3/4 by Numerical Approximation</h2>

14 <h2>Square Root of 3/4 by Numerical Approximation</h2>

16 <p>Numerical approximation is a method used to find a more precise<a>decimal</a>value for the square root of a number.</p>

15 <p>Numerical approximation is a method used to find a more precise<a>decimal</a>value for the square root of a number.</p>

17 <p><strong>Step 1:</strong>Approximate the square root of the numerator, √3 ≈ 1.732.</p>

16 <p><strong>Step 1:</strong>Approximate the square root of the numerator, √3 ≈ 1.732.</p>

18 <p><strong>Step 2:</strong>The square root of the denominator, √4, is 2.</p>

17 <p><strong>Step 2:</strong>The square root of the denominator, √4, is 2.</p>

19 <p><strong>Step 3:</strong>Divide the approximate square root of the numerator by the exact square root of the denominator: 1.732/2 = 0.866.</p>

18 <p><strong>Step 3:</strong>Divide the approximate square root of the numerator by the exact square root of the denominator: 1.732/2 = 0.866.</p>

20 <h2>Square Root of 3/4 by Prime Factorization Method</h2>

19 <h2>Square Root of 3/4 by Prime Factorization Method</h2>

21 <p>The<a>prime factorization</a>method is generally used for<a>whole numbers</a>, but it can help us understand the properties of the square roots involved.</p>

20 <p>The<a>prime factorization</a>method is generally used for<a>whole numbers</a>, but it can help us understand the properties of the square roots involved.</p>

22 <p><strong>Step 1:</strong>Prime factorization of 3 is itself, as it's a<a>prime number</a>.</p>

21 <p><strong>Step 1:</strong>Prime factorization of 3 is itself, as it's a<a>prime number</a>.</p>

23 <p><strong>Step 2:</strong>Prime factorization of 4 is 2 x 2.</p>

22 <p><strong>Step 2:</strong>Prime factorization of 4 is 2 x 2.</p>

24 <p><strong>Step 3:</strong>As we cannot form complete pairs for 3, it indicates the result will be irrational.</p>

23 <p><strong>Step 3:</strong>As we cannot form complete pairs for 3, it indicates the result will be irrational.</p>

25 <h2>Comparison with Whole Number Square Roots</h2>

24 <h2>Comparison with Whole Number Square Roots</h2>

26 <p>It is useful to compare the value of √(3/4) with the square roots of whole numbers to understand its relative size.</p>

25 <p>It is useful to compare the value of √(3/4) with the square roots of whole numbers to understand its relative size.</p>

27 <p><strong>Step 1:</strong>We know √1 = 1, which is<a>greater than</a>0.866.</p>

26 <p><strong>Step 1:</strong>We know √1 = 1, which is<a>greater than</a>0.866.</p>

28 <p><strong>Step 2:</strong>Therefore, √(3/4) ≈ 0.866 is<a>less than</a>1 but greater than √0.</p>

27 <p><strong>Step 2:</strong>Therefore, √(3/4) ≈ 0.866 is<a>less than</a>1 but greater than √0.</p>

29 <h2>Common Mistakes and How to Avoid Them in the Square Root of 3/4</h2>

28 <h2>Common Mistakes and How to Avoid Them in the Square Root of 3/4</h2>

30 <p>Students often make mistakes while finding the square root of fractions, such as not simplifying the fraction beforehand or confusing numerator and denominator. Now let us look at a few of those mistakes in detail.</p>

29 <p>Students often make mistakes while finding the square root of fractions, such as not simplifying the fraction beforehand or confusing numerator and denominator. Now let us look at a few of those mistakes 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 √(3/4)?</p>

31 <p>Can you help Max find the area of a square box if its side length is given as √(3/4)?</p>

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

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

34 <p>The area of the square is 0.75 square units.</p>

33 <p>The area of the square is 0.75 square units.</p>

35 <h3>Explanation</h3>

34 <h3>Explanation</h3>

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

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

37 <p>The side length is given as √(3/4).</p>

36 <p>The side length is given as √(3/4).</p>

38 <p>Area of the square = (√(3/4))^2 = 3/4 = 0.75.</p>

37 <p>Area of the square = (√(3/4))^2 = 3/4 = 0.75.</p>

39 <p>Therefore, the area of the square box is 0.75 square units.</p>

38 <p>Therefore, the area of the square box is 0.75 square units.</p>

40 <p>Well explained 👍</p>

39 <p>Well explained 👍</p>

41 <h3>Problem 2</h3>

40 <h3>Problem 2</h3>

42 <p>A square-shaped garden measures 3/4 square feet; if each of the sides is √(3/4), what will be the square feet of half of the garden?</p>

41 <p>A square-shaped garden measures 3/4 square feet; if each of the sides is √(3/4), what will be the square feet of half of the garden?</p>

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

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

44 <p>0.375 square feet</p>

43 <p>0.375 square feet</p>

45 <h3>Explanation</h3>

44 <h3>Explanation</h3>

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

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

47 <p>Dividing 3/4 by 2 = we get 3/8 = 0.375.</p>

46 <p>Dividing 3/4 by 2 = we get 3/8 = 0.375.</p>

48 <p>So half of the garden measures 0.375 square feet.</p>

47 <p>So half of the garden measures 0.375 square feet.</p>

49 <p>Well explained 👍</p>

48 <p>Well explained 👍</p>

50 <h3>Problem 3</h3>

49 <h3>Problem 3</h3>

51 <p>Calculate √(3/4) x 8.</p>

50 <p>Calculate √(3/4) x 8.</p>

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

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

53 <p>6.928</p>

52 <p>6.928</p>

54 <h3>Explanation</h3>

53 <h3>Explanation</h3>

55 <p>The first step is to find the square root of 3/4, which is approximately 0.866.</p>

54 <p>The first step is to find the square root of 3/4, which is approximately 0.866.</p>

56 <p>The second step is to multiply 0.866 by 8.</p>

55 <p>The second step is to multiply 0.866 by 8.</p>

57 <p>So 0.866 x 8 = 6.928.</p>

56 <p>So 0.866 x 8 = 6.928.</p>

58 <p>Well explained 👍</p>

57 <p>Well explained 👍</p>

59 <h3>Problem 4</h3>

58 <h3>Problem 4</h3>

60 <p>What will be the square root of (3/4 + 1/4)?</p>

59 <p>What will be the square root of (3/4 + 1/4)?</p>

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

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

62 <p>The square root is 1.</p>

61 <p>The square root is 1.</p>

63 <h3>Explanation</h3>

62 <h3>Explanation</h3>

64 <p>To find the square root, we need to find the sum of (3/4 + 1/4) 3/4 + 1/4 = 1, and then √1 = 1.</p>

63 <p>To find the square root, we need to find the sum of (3/4 + 1/4) 3/4 + 1/4 = 1, and then √1 = 1.</p>

65 <p>Therefore, the square root of (3/4 + 1/4) is 1.</p>

64 <p>Therefore, the square root of (3/4 + 1/4) is 1.</p>

66 <p>Well explained 👍</p>

65 <p>Well explained 👍</p>

67 <h3>Problem 5</h3>

66 <h3>Problem 5</h3>

68 <p>Find the perimeter of a rectangle if its length ‘l’ is √(3/4) units and the width ‘w’ is 1 unit.</p>

67 <p>Find the perimeter of a rectangle if its length ‘l’ is √(3/4) units and the width ‘w’ is 1 unit.</p>

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

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

70 <p>The perimeter of the rectangle is 3.732 units.</p>

69 <p>The perimeter of the rectangle is 3.732 units.</p>

71 <h3>Explanation</h3>

70 <h3>Explanation</h3>

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

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

73 <p>Perimeter = 2 × (√(3/4) + 1) = 2 × (0.866 + 1) = 2 × 1.866 = 3.732 units.</p>

72 <p>Perimeter = 2 × (√(3/4) + 1) = 2 × (0.866 + 1) = 2 × 1.866 = 3.732 units.</p>

74 <p>Well explained 👍</p>

73 <p>Well explained 👍</p>

75 <h2>FAQ on Square Root of 3/4</h2>

74 <h2>FAQ on Square Root of 3/4</h2>

76 <h3>1.What is √(3/4) in its simplest form?</h3>

75 <h3>1.What is √(3/4) in its simplest form?</h3>

77 <p>The simplest form of √(3/4) is √3/2.</p>

76 <p>The simplest form of √(3/4) is √3/2.</p>

78 <h3>2.Mention the factors of 3/4.</h3>

77 <h3>2.Mention the factors of 3/4.</h3>

79 <h3>3.Calculate the square of 3/4.</h3>

78 <h3>3.Calculate the square of 3/4.</h3>

80 <p>We get the square of 3/4 by multiplying the number by itself, that is (3/4) x (3/4) = 9/16.</p>

79 <p>We get the square of 3/4 by multiplying the number by itself, that is (3/4) x (3/4) = 9/16.</p>

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

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

82 <p>No, 3/4 is a fraction, and the concept of prime numbers applies only to whole numbers.</p>

81 <p>No, 3/4 is a fraction, and the concept of prime numbers applies only to whole numbers.</p>

83 <h3>5.Is 3/4 a rational number?</h3>

82 <h3>5.Is 3/4 a rational number?</h3>

84 <p>Yes, 3/4 is a<a>rational number</a>because it can be expressed as a fraction of two integers, with a non-zero denominator.</p>

83 <p>Yes, 3/4 is a<a>rational number</a>because it can be expressed as a fraction of two integers, with a non-zero denominator.</p>

85 <h2>Important Glossaries for the Square Root of 3/4</h2>

84 <h2>Important Glossaries for the Square Root of 3/4</h2>

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

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

87 </ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.</li>

86 </ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.</li>

88 </ul><ul><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>

87 </ul><ul><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>

89 </ul><ul><li><strong>Numerical approximation:</strong>This is a method of finding an approximate value of a number, often used for square roots to find a decimal representation.</li>

88 </ul><ul><li><strong>Numerical approximation:</strong>This is a method of finding an approximate value of a number, often used for square roots to find a decimal representation.</li>

90 </ul><ul><li><strong>Simplification:</strong>Simplification involves reducing a mathematical expression or fraction to its simplest form.</li>

89 </ul><ul><li><strong>Simplification:</strong>Simplification involves reducing a mathematical expression or fraction to its simplest form.</li>

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

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

92 <p>▶</p>

91 <p>▶</p>

93 <h2>Jaskaran Singh Saluja</h2>

92 <h2>Jaskaran Singh Saluja</h2>

94 <h3>About the Author</h3>

93 <h3>About the Author</h3>

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>

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>

96 <h3>Fun Fact</h3>

95 <h3>Fun Fact</h3>

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

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