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2 <p>Last updated on<strong>December 15, 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 and finance. Here, we will discuss the square root of 81/400.</p>

4 <h2>What is the Square Root of 81/400?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>.</p>

6 <p>81/400 is a<a>perfect square</a><a>fraction</a>.</p>

7 <p>The square root of 81/400 can be expressed in both radical and fractional form.</p>

8 <p>In radical form, it is expressed as √(81/400), whereas in fractional form, it is expressed as (81/400)^(1/2).</p>

9 <p>√(81/400) = 9/20, 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>

10 <h2>Finding the Square Root of 81/400</h2>

11 <p>The<a>prime factorization</a>method is used for perfect square numbers.</p>

12 <p>For perfect square fractions like 81/400, the<a>square root</a>can be determined by taking the square root of the<a>numerator</a>and the<a>denominator</a>separately.</p>

13 <p>Let us now learn the following methods:</p>

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

15 <li>Long<a>division</a>method </li>

16 <li>Approximation method</li>

17 </ul><h2>Square Root of 81/400 by Prime Factorization Method</h2>

18 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number.</p>

19 <p>Now let us look at how 81 and 400 are broken down into their prime factors:</p>

20 <p><strong>Step 1:</strong>Finding the prime factors of 81 and 400.</p>

21 <p>Breaking it down, we get 81 = 3 x 3 x 3 x 3 = 34, and 400 = 2 x 2 x 2 x 2 x 5 x 5 = 24 x 52.</p>

22 <p><strong>Step 2:</strong>Now we find the square root by taking the square root of the prime factors.</p>

23 <p>√(81/400) = √81/√400 = 32/22 x 5 = 9/20.</p>

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26 <h2>Square Root of 81/400 by Long Division Method</h2>

25 <h2>Square Root of 81/400 by Long Division Method</h2>

27 <p>The<a>long division</a>method is particularly used for non-perfect square numbers, but it can also be used for fractions.</p>

26 <p>The<a>long division</a>method is particularly used for non-perfect square numbers, but it can also be used for fractions.</p>

28 <p>In this method, we should check the perfect square numbers for the given fraction.</p>

27 <p>In this method, we should check the perfect square numbers for the given fraction.</p>

29 <p>Let us now learn how to find the square root using the long division method:</p>

28 <p>Let us now learn how to find the square root using the long division method:</p>

30 <p><strong>Step 1:</strong>Calculate the square roots of the numerator and the denominator separately using the long division method.</p>

29 <p><strong>Step 1:</strong>Calculate the square roots of the numerator and the denominator separately using the long division method.</p>

31 <p><strong>Step 2:</strong>The square root of 81 is 9 and the square root of 400 is 20.</p>

30 <p><strong>Step 2:</strong>The square root of 81 is 9 and the square root of 400 is 20.</p>

32 <p><strong>Step 3:</strong>Combine the results to get the square root of the fraction: 9/20.</p>

31 <p><strong>Step 3:</strong>Combine the results to get the square root of the fraction: 9/20.</p>

33 <h2>Square Root of 81/400 by Approximation Method</h2>

32 <h2>Square Root of 81/400 by Approximation Method</h2>

34 <p>The approximation method is another method for finding square roots, but since 81/400 is a perfect square fraction, we can directly find its square root without approximation.</p>

33 <p>The approximation method is another method for finding square roots, but since 81/400 is a perfect square fraction, we can directly find its square root without approximation.</p>

35 <p><strong>Step 1:</strong>Recognize that 81 is the square of 9 and 400 is the square of 20.</p>

34 <p><strong>Step 1:</strong>Recognize that 81 is the square of 9 and 400 is the square of 20.</p>

36 <p><strong>Step 2:</strong>Therefore, √(81/400) = 9/20.</p>

35 <p><strong>Step 2:</strong>Therefore, √(81/400) = 9/20.</p>

37 <h2>Common Mistakes and How to Avoid Them in the Square Root of 81/400</h2>

36 <h2>Common Mistakes and How to Avoid Them in the Square Root of 81/400</h2>

38 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or incorrectly simplifying the fraction.</p>

37 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or incorrectly simplifying the fraction.</p>

39 <p>Now let us look at a few of those mistakes that students tend to make in detail.</p>

38 <p>Now let us look at a few of those mistakes that students tend to make in detail.</p>

40 <h3>Problem 1</h3>

39 <h3>Problem 1</h3>

41 <p>Can you help Max find the area of a square box if its side length is given as √(81/400)?</p>

40 <p>Can you help Max find the area of a square box if its side length is given as √(81/400)?</p>

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

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

43 <p>The area of the square is 0.2025 square units.</p>

42 <p>The area of the square is 0.2025 square units.</p>

44 <h3>Explanation</h3>

43 <h3>Explanation</h3>

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

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

46 <p>The side length is given as √(81/400).</p>

45 <p>The side length is given as √(81/400).</p>

47 <p>Area of the square = (9/20) x (9/20) = 0.2025.</p>

46 <p>Area of the square = (9/20) x (9/20) = 0.2025.</p>

48 <p>Therefore, the area of the square box is 0.2025 square units.</p>

47 <p>Therefore, the area of the square box is 0.2025 square units.</p>

49 <p>Well explained 👍</p>

48 <p>Well explained 👍</p>

50 <h3>Problem 2</h3>

49 <h3>Problem 2</h3>

51 <p>A square-shaped garden measuring 81/400 square feet is built; if each of the sides is √(81/400), what will be the square feet of half of the garden?</p>

50 <p>A square-shaped garden measuring 81/400 square feet is built; if each of the sides is √(81/400), what will be the square feet of half of the garden?</p>

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

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

53 <p>0.10125 square feet</p>

52 <p>0.10125 square feet</p>

54 <h3>Explanation</h3>

53 <h3>Explanation</h3>

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

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

56 <p>Dividing 81/400 by 2 = 0.10125.</p>

55 <p>Dividing 81/400 by 2 = 0.10125.</p>

57 <p>So half of the garden measures 0.10125 square feet.</p>

56 <p>So half of the garden measures 0.10125 square feet.</p>

58 <p>Well explained 👍</p>

57 <p>Well explained 👍</p>

59 <h3>Problem 3</h3>

58 <h3>Problem 3</h3>

60 <p>Calculate √(81/400) x 5.</p>

59 <p>Calculate √(81/400) x 5.</p>

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

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

62 <p>2.25</p>

61 <p>2.25</p>

63 <h3>Explanation</h3>

62 <h3>Explanation</h3>

64 <p>The first step is to find the square root of 81/400, which is 9/20.</p>

63 <p>The first step is to find the square root of 81/400, which is 9/20.</p>

65 <p>The second step is to multiply 9/20 by 5.</p>

64 <p>The second step is to multiply 9/20 by 5.</p>

66 <p>So 9/20 x 5 = 2.25.</p>

65 <p>So 9/20 x 5 = 2.25.</p>

67 <p>Well explained 👍</p>

66 <p>Well explained 👍</p>

68 <h3>Problem 4</h3>

67 <h3>Problem 4</h3>

69 <p>What will be the square root of (81/400 + 19/400)?</p>

68 <p>What will be the square root of (81/400 + 19/400)?</p>

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

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

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

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

72 <h3>Explanation</h3>

71 <h3>Explanation</h3>

73 <p>To find the square root, we need to find the sum of (81/400 + 19/400). 81/400 + 19/400 = 100/400 = 1/4, and then √(1/4) = 1/2.</p>

72 <p>To find the square root, we need to find the sum of (81/400 + 19/400). 81/400 + 19/400 = 100/400 = 1/4, and then √(1/4) = 1/2.</p>

74 <p>Therefore, the square root of (81/400 + 19/400) is ±1/2.</p>

73 <p>Therefore, the square root of (81/400 + 19/400) is ±1/2.</p>

75 <p>Well explained 👍</p>

74 <p>Well explained 👍</p>

76 <h3>Problem 5</h3>

75 <h3>Problem 5</h3>

77 <p>Find the perimeter of a rectangle if its length ‘l’ is √(81/400) units and the width ‘w’ is 3/4 units.</p>

76 <p>Find the perimeter of a rectangle if its length ‘l’ is √(81/400) units and the width ‘w’ is 3/4 units.</p>

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

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

79 <p>We find the perimeter of the rectangle as 2.1 units.</p>

78 <p>We find the perimeter of the rectangle as 2.1 units.</p>

80 <h3>Explanation</h3>

79 <h3>Explanation</h3>

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

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

82 <p>Perimeter = 2 × (9/20 + 3/4) = 2 × (9/20 + 15/20) = 2 × (24/20) = 2 × 1.2 = 2.4 units.</p>

81 <p>Perimeter = 2 × (9/20 + 3/4) = 2 × (9/20 + 15/20) = 2 × (24/20) = 2 × 1.2 = 2.4 units.</p>

83 <p>Well explained 👍</p>

82 <p>Well explained 👍</p>

84 <h2>FAQ on Square Root of 81/400</h2>

83 <h2>FAQ on Square Root of 81/400</h2>

85 <h3>1.What is √(81/400) in its simplest form?</h3>

84 <h3>1.What is √(81/400) in its simplest form?</h3>

86 <p>The simplest form of √(81/400) is 9/20.</p>

85 <p>The simplest form of √(81/400) is 9/20.</p>

87 <h3>2.Mention the factors of 81 and 400.</h3>

86 <h3>2.Mention the factors of 81 and 400.</h3>

88 <p>Factors of 81 are 1, 3, 9, 27, and 81.</p>

87 <p>Factors of 81 are 1, 3, 9, 27, and 81.</p>

89 <p>Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400.</p>

88 <p>Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400.</p>

90 <h3>3.Calculate the square of 81/400.</h3>

89 <h3>3.Calculate the square of 81/400.</h3>

91 <p>We get the square of 81/400 by multiplying the number by itself, that is (81/400) x (81/400) = 6561/160000.</p>

90 <p>We get the square of 81/400 by multiplying the number by itself, that is (81/400) x (81/400) = 6561/160000.</p>

92 <h3>4.Is 81/400 a prime fraction?</h3>

91 <h3>4.Is 81/400 a prime fraction?</h3>

93 <p>81/400 is not a prime fraction, as both the numerator and the denominator have more than one factor.</p>

92 <p>81/400 is not a prime fraction, as both the numerator and the denominator have more than one factor.</p>

94 <h3>5.Is 81/400 a rational number?</h3>

93 <h3>5.Is 81/400 a rational number?</h3>

95 <p>Yes, 81/400 is a rational number because it can be expressed as a fraction of integers.</p>

94 <p>Yes, 81/400 is a rational number because it can be expressed as a fraction of integers.</p>

96 <h2>Important Glossaries for the Square Root of 81/400</h2>

95 <h2>Important Glossaries for the Square Root of 81/400</h2>

97 <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>

96 <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>

98 </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>

97 </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>

99 </ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 81 is a perfect square because it is 92.</li>

98 </ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 81 is a perfect square because it is 92.</li>

100 </ul><ul><li><strong>Fraction:</strong>A fraction is a part of a whole expressed using a numerator and a denominator. For example, 81/400 is a fraction.</li>

99 </ul><ul><li><strong>Fraction:</strong>A fraction is a part of a whole expressed using a numerator and a denominator. For example, 81/400 is a fraction.</li>

101 </ul><ul><li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number then it is called a decimal. For example, 0.45, 0.75, and 0.95 are decimals.</li>

100 </ul><ul><li><strong>Decimal:</strong>If a number has a whole number and a fraction in a single number then it is called a decimal. For example, 0.45, 0.75, and 0.95 are decimals.</li>

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

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

103 <p>▶</p>

102 <p>▶</p>

104 <h2>Jaskaran Singh Saluja</h2>

103 <h2>Jaskaran Singh Saluja</h2>

105 <h3>About the Author</h3>

104 <h3>About the Author</h3>

106 <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>

105 <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>

107 <h3>Fun Fact</h3>

106 <h3>Fun Fact</h3>

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

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