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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>The square root of 27 is the inverse operation of squaring a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 27. It contains both positive and a negative root, where the positive root is called the principal square root.</p>

4 <h2>What Is the Square Root of 27?</h2>

5 <p>The<a>square</a>root<a>of</a>27 is ±5.19615242271.The positive value, 5.19615242271 is the solution of the<a>equation</a>x2 = 27.</p>

6 <p>As defined, the square root is just the inverse of squaring a<a>number</a>, so, squaring 5.19615242271 will result in 27. The square root of 27 is expressed as √27 in radical form, where the ‘√’ sign is called “radical” sign. In<a>exponential form</a>, it is written as (27)1/2 </p>

7 <h2>Finding the Square Root of 27</h2>

8 <p>We can find the<a>square root</a>of 27 through various methods. They are:</p>

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

10 </ul><ul><li>Long<a>division</a>method</li>

11 </ul><ul><li>Approximation/Estimation method</li>

12 </ul><h3>Square Root of 27 By Prime Factorization Method</h3>

13 <p>The<a>prime factorization</a>of 27 involves breaking down a number into its<a>factors</a>. Divide 27 by<a>prime numbers</a>, and continue to divide the quotients until they can’t be separated anymore.</p>

14 <p>After factorizing 27, make pairs out of the factors to get the square root. If there exists numbers which cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs</p>

15 <p>So, Prime factorization of 27 = 3 × 3 × 3 </p>

16 <p> But for 27, a pair of factor 3 can be obtained and a single 3 is remaining</p>

17 <p>So, it can be expressed as √27 = √3 × √(3 × 3) = 3√3</p>

18 <p> 3√3 is the simplest radical form of √27</p>

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21 <h3>Square Root of 27 By Long Division Method</h3>

20 <h3>Square Root of 27 By Long Division Method</h3>

22 <p>This is a method used for obtaining the square root for non-<a>perfect squares</a>, mainly. It usually involves the division of the<a>dividend</a>by the<a>divisor</a>, getting a<a>quotient</a>and a<a>remainder</a>too sometimes.</p>

21 <p>This is a method used for obtaining the square root for non-<a>perfect squares</a>, mainly. It usually involves the division of the<a>dividend</a>by the<a>divisor</a>, getting a<a>quotient</a>and a<a>remainder</a>too sometimes.</p>

23 <p>Follow the steps to calculate the square root of 27:</p>

22 <p>Follow the steps to calculate the square root of 27:</p>

24 <p><strong>Step 1 :</strong>Write the number 27, and draw a bar above the pair of digits from right to left.</p>

23 <p><strong>Step 1 :</strong>Write the number 27, and draw a bar above the pair of digits from right to left.</p>

25 <p> <strong>Step 2 :</strong>Now, find the greatest number whose square is<a>less than</a>or equal to. Here, it is 5, Because 52=25 < 27</p>

24 <p> <strong>Step 2 :</strong>Now, find the greatest number whose square is<a>less than</a>or equal to. Here, it is 5, Because 52=25 < 27</p>

26 <p><strong>Step 3 :</strong>Now divide 27 by 5 (the number we got from Step 2) such that we get 5 as quotient, and we get a remainder. Double the divisor 5, we get 10 and then the largest possible number A1=1 is chosen such that when 1 is written beside the new divisor, 10, a 3-digit number is formed →101 and multiplying 1 with 101 gives 101 which is less than 200.</p>

25 <p><strong>Step 3 :</strong>Now divide 27 by 5 (the number we got from Step 2) such that we get 5 as quotient, and we get a remainder. Double the divisor 5, we get 10 and then the largest possible number A1=1 is chosen such that when 1 is written beside the new divisor, 10, a 3-digit number is formed →101 and multiplying 1 with 101 gives 101 which is less than 200.</p>

27 <p>Repeat the process until you reach remainder 0</p>

26 <p>Repeat the process until you reach remainder 0</p>

28 <p>We are left with the remainder, 1584 (refer to the picture), after some iterations and keeping the division till here, at this point </p>

27 <p>We are left with the remainder, 1584 (refer to the picture), after some iterations and keeping the division till here, at this point </p>

29 <p> <strong>Step 4 :</strong>The quotient obtained is the square root. In this case, it is 5.196…</p>

28 <p> <strong>Step 4 :</strong>The quotient obtained is the square root. In this case, it is 5.196…</p>

30 <h3>Square Root of 27 By Approximation Method</h3>

29 <h3>Square Root of 27 By Approximation Method</h3>

31 <p>Approximation or<a>estimation</a>of square root is not the exact square root, but it is an estimate. Here, through this method, an approximate value of square root is found by guessing.</p>

30 <p>Approximation or<a>estimation</a>of square root is not the exact square root, but it is an estimate. Here, through this method, an approximate value of square root is found by guessing.</p>

32 <p>Follow the steps below:</p>

31 <p>Follow the steps below:</p>

33 <p><strong>Step 1 :</strong>Identify the square roots of the perfect squares above and below 27</p>

32 <p><strong>Step 1 :</strong>Identify the square roots of the perfect squares above and below 27</p>

34 <p>Below : 25→ square root of 25 = 5 ……..(<a>i</a>)</p>

33 <p>Below : 25→ square root of 25 = 5 ……..(<a>i</a>)</p>

35 <p>Above : 36 →square root of 36 = 6 ……..(ii)</p>

34 <p>Above : 36 →square root of 36 = 6 ……..(ii)</p>

36 <p><strong>Step 2 :</strong>Divide 27 with one of 5 or 6 f we choose 5, and divide 27 by 5,</p>

35 <p><strong>Step 2 :</strong>Divide 27 with one of 5 or 6 f we choose 5, and divide 27 by 5,</p>

37 <p>we get 5.4 …….(iii)</p>

36 <p>we get 5.4 …….(iii)</p>

38 <p> <strong>Step 3:</strong>Find the<a>average</a>of 5 (from (i)) and 5.4 (from (iii))</p>

37 <p> <strong>Step 3:</strong>Find the<a>average</a>of 5 (from (i)) and 5.4 (from (iii))</p>

39 <p>(5+5.4)/2 = 5.2</p>

38 <p>(5+5.4)/2 = 5.2</p>

40 <p>Hence, 5.2 is the approximate square root of 27 </p>

39 <p>Hence, 5.2 is the approximate square root of 27 </p>

41 <h2>Common Mistakes and How to Avoid Them in the Square Root of 27</h2>

40 <h2>Common Mistakes and How to Avoid Them in the Square Root of 27</h2>

42 <p>When we find the square root of 27, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions. </p>

41 <p>When we find the square root of 27, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions. </p>

42 + <h2>Download Worksheets</h2>

43 <h3>Problem 1</h3>

44 <p>Simplify √27 + √18 ?</p>

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

46 <p>√27 + √18</p>

47 <p>= 3√3 + 3√2</p>

48 <p>= 3(√3 + √2)</p>

49 <p>Answer : 3(√3 + √2) </p>

50 <h3>Explanation</h3>

51 <p>firstly, we found the values of the square roots of 27 and 18, then took 3 outside as common. </p>

52 <p>Well explained 👍</p>

53 <h3>Problem 2</h3>

54 <p>Find the length of a side of a square whose area is 27 cm^2 ?</p>

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

56 <p>Given, the area = 27 cm2</p>

57 <p>We know that, (side of a square)2 = area of square</p>

58 <p>Or, (side of a square)2 = 27</p>

59 <p>Or, (side of a square)= √27</p>

60 <p>Or, side of a square = ± 5.1961</p>

61 <p>But, length of a square is a positive quantity only, so, length of the side is 5.1961 cm.</p>

62 <p>Answer: 5.1961 cm </p>

63 <h3>Explanation</h3>

64 <p>We know that, (side of a square)2 = area of square. Here, we are given with the area of the square, so, we can easily find out its square root because its Square root is the measure of the side of the square. </p>

65 <p>Well explained 👍</p>

66 <h3>Problem 3</h3>

67 <p>Which is greater √27 or √26 ?</p>

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

69 <p>Approximate both values </p>

70 <p>√27 ≅ 5.196</p>

71 <p>√26 ≅ 5.099</p>

72 <p>5.196 > 5.099</p>

73 <p>hence √27 > √26</p>

74 <p>Answer: √27 is greater than √26</p>

75 <h3>Explanation</h3>

76 <p>It is obvious that √27 is greater than √26, but still we should find out the exact values and compare. </p>

77 <p>Well explained 👍</p>

78 <h3>Problem 4</h3>

79 <p>If y=√27, find y^2</p>

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

81 <p>firstly, y=√27= 5.1961</p>

82 <p>Now, squaring y, we get, </p>

83 <p>y2= (5.1961)2=27</p>

84 <p>or, y2=27</p>

85 <p>Answer : 27 </p>

86 <h3>Explanation</h3>

87 <p> squaring “y” which is same as squaring the value of √27 resulted to 27 </p>

88 <p>Well explained 👍</p>

89 <h3>Problem 5</h3>

90 <p>Calculate (√27/5 + √27/2)</p>

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

92 <p>√27/5 + √27/2</p>

93 <p>= 5.1961/ 5 + 5.1961/2</p>

94 <p>= 1.03922 + 2.59805</p>

95 <p>= 3.63727</p>

96 <p>Answer : 3.63727 </p>

97 <h3>Explanation</h3>

98 <p>From the given expression, we first found the value of square root of 27 then solved by simple divisions and then simple addition. </p>

99 <p>Well explained 👍</p>

100 <h2>FAQs on Square Root of 27</h2>

101 <h3>1.What is the square root of 27?</h3>

102 <p>The square root of 27 is ±3√3, which is equal to ±5.19615242271 </p>

103 <h3>2.What is √27 ⤫ √3 ?</h3>

104 <h3>3.Is 27 a perfect square or non-perfect square?</h3>

105 <p> 27 is a non-perfect square, since 27 =(5.19615242271)2. </p>

106 <h3>4.Is the square root of 27 a rational or irrational number?</h3>

107 <p>The square root of 27 is ±5.19615242271 . So, 5.19615242271 is an irrational number, since it cannot be obtained by dividing two<a>integers</a>and cannot be written in the form p/q, where p and q are integers. </p>

108 <h3>5.What is the principal square root of 27?</h3>

109 <p>The principal square root of 27 is 5.19615242271, the positive value, but not -5.19615242271. </p>

110 <h3>6. What are the factors of 27?</h3>

111 <p> factors of 27 are 1,3,9,27 </p>

112 <h2>Important Glossaries for Square Root of 27</h2>

113 <ul><li><strong>Exponential form: </strong>An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent. Ex: 2 × 2 × 2 × 2 = 16 Or, 2 4 = 16, where 2 is the base, 4 is the exponent </li>

114 </ul><ul><li><strong>Prime Factorization:</strong> Expressing the given expression as a product of its factors. Ex: 48=2 × 2 × 2 × 2 × 3</li>

115 </ul><ul><li><strong>Prime Numbers:</strong>Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....</li>

116 </ul><ul><li><strong>Rational numbers and Irrational numbers:</strong>The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. </li>

117 </ul><ul><li><strong>Perfect and non-perfect square numbers:</strong>Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :3, 8, 24</li>

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

119 <p>▶</p>

120 <h2>Jaskaran Singh Saluja</h2>

121 <h3>About the Author</h3>

122 <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>

123 <h3>Fun Fact</h3>

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