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1 - <p>665 Learners</p>

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

3 <p>The square root of 18 is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 18. The number 18 has a unique non-negative square root, called the principal square root.</p>

4 <h2>What Is the Square Root of 18?</h2>

5 <p>The<a>square</a>root<a>of</a>18 is ±4.24264068712, where is 4.24264068712 the positive solution of the<a>equation</a>x2 = 18.</p>

6 <p>Finding the square root is just the inverse of squaring a<a>number</a>and hence, squaring 4.24264068712 will result in 18.</p>

7 <p>The square root of 18 is written as √18 in radical form, where the ‘√’ sign is called the “radical” sign. In<a>exponential form</a>, it is written as (18)1/2 </p>

8 <h2>Finding the Square Root of 18</h2>

9 <p>We can find the<a>square root</a>of 18 through various methods. They are:</p>

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

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

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

13 </ul><h3>Square Root of 18 By Prime Factorization Method</h3>

14 <p>The<a>prime factorization</a>of 18 is done by dividing 18 by<a>prime numbers</a>and continuing to divide the quotients until they can’t be separated anymore.</p>

15 <p>After factorizing 18, make pairs out of the<a>factors</a>to get the square root. If there exist numbers that cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs</p>

16 <p>So, Prime factorization of 18 = 3 × 3 × 2 </p>

17 <p>But here in the case of 18, a pair of factor 3 can be obtained but a single 2 is remaining</p>

18 <p>So, it can be expressed as √18 = √(3 × 3 × 2) = 3√2</p>

19 <p> 3√2 is the simplest radical form of √18</p>

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22 <h3>Square Root of 18 By Long Division Method</h3>

21 <h3>Square Root of 18 By Long Division Method</h3>

23 <p>This method is 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>

22 <p>This method is 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>

24 <p>Follow the steps to calculate the square root of 18:</p>

23 <p>Follow the steps to calculate the square root of 18:</p>

25 <p><strong> Step 1:</strong>Write the number 18, and draw a bar above the pair of digits from right to left.</p>

24 <p><strong> Step 1:</strong>Write the number 18, and draw a bar above the pair of digits from right to left.</p>

26 <p> <strong>Step 2:</strong>Now, find the greatest number whose square is<a>less than</a>or equal to. Here, it is 4, Because 42=16 < 18.</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 4, Because 42=16 < 18.</p>

27 <p><strong>Step 3 :</strong>Now divide 18 by 4 (the number we got from Step 2) such that we get 4 as quotient and we get a remainder.Double the divisor 4, we get 8, and then the largest possible number A1=2 is chosen such that when 2 is written beside the new divisor, 8, a 2-digit number is formed →82, and multiplying 2 with 82 gives 164 which is less than 200.</p>

26 <p><strong>Step 3 :</strong>Now divide 18 by 4 (the number we got from Step 2) such that we get 4 as quotient and we get a remainder.Double the divisor 4, we get 8, and then the largest possible number A1=2 is chosen such that when 2 is written beside the new divisor, 8, a 2-digit number is formed →82, and multiplying 2 with 82 gives 164 which is less than 200.</p>

28 <p>Repeat the process until you reach the remainder of 0.</p>

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

29 <p>We are left with the remainder, 34524 (refer to the picture), after some iteration and keeping the division till here, at this point </p>

28 <p>We are left with the remainder, 34524 (refer to the picture), after some iteration and keeping the division till here, at this point </p>

30 <p> <strong>Step 4 :</strong>The quotient obtained is the square root. In this case, it is 4.2426….</p>

29 <p> <strong>Step 4 :</strong>The quotient obtained is the square root. In this case, it is 4.2426….</p>

31 <h3>Square Root of 18 By Approximation</h3>

30 <h3>Square Root of 18 By Approximation</h3>

32 <p>Approximation or<a>estimation</a>of the 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>

31 <p>Approximation or<a>estimation</a>of the 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>

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

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

34 <p><strong>Step 1:</strong> identify the square roots of the perfect squares above and below 18</p>

33 <p><strong>Step 1:</strong> identify the square roots of the perfect squares above and below 18</p>

35 <p> Below : 16→ square root of 16 = 4 ……..(<a>i</a>) Above : 25 →square root of 25 = 5 ……..(ii)</p>

34 <p> Below : 16→ square root of 16 = 4 ……..(<a>i</a>) Above : 25 →square root of 25 = 5 ……..(ii)</p>

36 <p><strong>Step 2:</strong>Dividing 18 with one of 4 or 5. If we choose 4 </p>

35 <p><strong>Step 2:</strong>Dividing 18 with one of 4 or 5. If we choose 4 </p>

37 <p> We get 4.5 when 18 is divided by 4 …….(iii)</p>

36 <p> We get 4.5 when 18 is divided by 4 …….(iii)</p>

38 <p> <strong>Step 3: </strong> find the<a>average</a>of 4 (from (i)) and 4.5 (from (iii))</p>

37 <p> <strong>Step 3: </strong> find the<a>average</a>of 4 (from (i)) and 4.5 (from (iii))</p>

39 <p> (4+4.5)/2 = 4.25 </p>

38 <p> (4+4.5)/2 = 4.25 </p>

40 <p> Hence, 4.25 is the approximate square root of 18 </p>

39 <p> Hence, 4.25 is the approximate square root of 18 </p>

41 <h2>Common Mistakes and How to Avoid Them in the Square Root of 18</h2>

40 <h2>Common Mistakes and How to Avoid Them in the Square Root of 18</h2>

42 <p>When we find the square root of 18, 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 18, 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>if x= √18, what is x^2-8 ?</p>

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

46 <p>x= √18</p>

47 <p>⇒ x2 = 18</p>

48 <p>⇒ x2-8 = 18-8</p>

49 <p> ⇒ x2-8 = 10</p>

50 <p>Answer : 10 </p>

51 <h3>Explanation</h3>

52 <p>we did the square of the given value of x and then subtracted 8 from it. </p>

53 <p>Well explained 👍</p>

54 <h3>Problem 2</h3>

55 <p>Find the length of a side of a square whose area is 18 cm^2</p>

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

57 <p> Given, the area = 18 cm2</p>

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

59 <p>Or, (side of a square)2 = 18</p>

60 <p>Or, (side of a square)= √18</p>

61 <p>Or, the side of a square = ±4.226</p>

62 <p>But, length of a square is a positive quantity only, so, length of the side is 4.2426 cm.</p>

63 <p>Answer: 4.2426 cm</p>

64 <h3>Explanation</h3>

65 <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>

66 <p>Well explained 👍</p>

67 <h3>Problem 3</h3>

68 <p>Simplify (√18 + √18) ⤫ √18</p>

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

70 <p>(√18 + √18) ⤫ √18</p>

71 <p>= (4.2426 + 4.2426) ⤫ 4.2426</p>

72 <p>= 8.4852 ⤫ 4.2426</p>

73 <p>= 35.9993</p>

74 <p>Answer: 35.9993 </p>

75 <h3>Explanation</h3>

76 <p>We first solved the part inside the brackets, i.e., √18 + √18, which resulted into 8.4852 and then multiplying it with √18 which is 4.2426 we get 35.9993 </p>

77 <p>Well explained 👍</p>

78 <h3>Problem 4</h3>

79 <p>If y=√18, find y^2</p>

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

81 <p> firstly, y=√18= 4.2426</p>

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

83 <p>y2= (4.2426)2=18</p>

84 <p>or, y2=18</p>

85 <p>Answer : 18 </p>

86 <h3>Explanation</h3>

87 <p>squaring “y” which is same as squaring the value of √18 resulted to 18.</p>

88 <p>Well explained 👍</p>

89 <h3>Problem 5</h3>

90 <p>Calculate (√18/4 + √18/5)</p>

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

92 <p>√18/4 + √18/5</p>

93 <p>= 4.2426/ 3 + 4.2426</p>

94 <p>= 1.4142 + 0.84852</p>

95 <p>= 2.26272</p>

96 <p>Answer : 2.26272 </p>

97 <h3>Explanation</h3>

98 <p>From the given expression, we first found the value of square root of 18 then solved by simple divisions and then simple addition</p>

99 <p>Well explained 👍</p>

100 <h2>FAQs on Square Root of 18</h2>

101 <h3>1.How to write the square root of 18?</h3>

102 <p>The square root of 18 is written as √18 </p>

103 <h3>2.Is the square root of 18 a whole number?</h3>

104 <p> No, 4.24264068712 the square root of 18, is not a<a>whole number</a>.</p>

105 <h3>3.Is 18 a perfect square or a non-perfect square?</h3>

106 <p>18 is a non-perfect square, since 18 =(4.24264068712)2. </p>

107 <h3>4.Is the square root of 18 a rational or irrational number?</h3>

108 <p>The square root of 18 is ±4.24264068712 . So, 4.24264068712 is an <a>irrational number</a>, 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>

109 <h3>5.What is the principal square root of 18?</h3>

110 <p>The principal square root of 18 is 4.24264068712, the positive value, but not -4.24264068712</p>

111 <h3>6.√18 falls between which two perfect squares?</h3>

112 <p>√18 = 4.24264068712 falls between two perfect squares → 4 and 9 </p>

113 <h2>Important Glossaries for Square Root of 18</h2>

114 <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>

115 </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>

116 </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>

117 </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>

118 </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>

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

120 <p>▶</p>

121 <h2>Jaskaran Singh Saluja</h2>

122 <h3>About the Author</h3>

123 <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>

124 <h3>Fun Fact</h3>

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