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

3 <p>The square root of 14 is the inverse operation of squaring a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 14. 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 14?</h2>

5 <p>The<a>square</a>root of 14 is ±3.74165738677.The positive value,3.74165738677 is the solution of the<a>equation</a>x2 = 14. As defined, the square root is just the inverse of squaring a<a>number</a>, so, squaring 3.74165738677 will result in 14. The square root of 14 is expressed as √14 in radical form, where the ‘√’ sign is called “radical” sign. In<a>exponential form</a>, it is written as (14)1/2 </p>

6 <h2>Finding the Square Root of 14</h2>

7 <p>We can find the<a>square root</a>of 14 through various methods. They are:</p>

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

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

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

11 </ul><h3>Square Root of 14 By Prime Factorization Method</h3>

12 <p>The<a>prime factorization</a>of 14 involves breaking down a number into its<a>factors</a>. Divide 14 by<a>prime numbers</a>, and continue to divide the quotients until they can’t be separated anymore. After factorizing 14, 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>

13 <p>So, Prime factorization of 14 =2 × 7 </p>

14 <p>for 14, no pairs of factors are obtained, but a single 2 and a single 7 are obtained.</p>

15 <p>So, it can be expressed as √14 = √(2 × 7) = √14</p>

16 <p>√14 is the simplest radical form of √14 </p>

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19 <h3>Square Root of 14 by Long Division Method</h3>

18 <h3>Square Root of 14 by Long Division Method</h3>

20 <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>

19 <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>Follow the steps to calculate the square root of 14:</p>

20 <p>Follow the steps to calculate the square root of 14:</p>

22 <p><strong>Step 1 :</strong>Write the number 14, and draw a bar above the pair of digits from right to left.</p>

21 <p><strong>Step 1 :</strong>Write the number 14, and draw a bar above the pair of digits from right to left.</p>

23 <p> <strong>Step 2 :</strong>Now, find the greatest number whose square is<a>less than</a>or equal to 14. Here, it is 3, Because 32=9 < 14</p>

22 <p> <strong>Step 2 :</strong>Now, find the greatest number whose square is<a>less than</a>or equal to 14. Here, it is 3, Because 32=9 < 14</p>

24 <p><strong>Step 3 :</strong>Now divide 14 by 3 (the number we got from Step 2) such that we get 3 as quotient, and we get a remainder. Double the divisor 3, we get 6 and then the largest possible number A1=7 is chosen such that when 7 is written beside the new divisor, 6, a 2-digit number is formed →67 and multiplying 7 with 67 gives 469 which is less than 500.</p>

23 <p><strong>Step 3 :</strong>Now divide 14 by 3 (the number we got from Step 2) such that we get 3 as quotient, and we get a remainder. Double the divisor 3, we get 6 and then the largest possible number A1=7 is chosen such that when 7 is written beside the new divisor, 6, a 2-digit number is formed →67 and multiplying 7 with 67 gives 469 which is less than 500.</p>

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

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

26 <p>We are left with the remainder, 4919 (refer to the picture), after some iterations and keeping the division till here, at this point </p>

25 <p>We are left with the remainder, 4919 (refer to the picture), after some iterations and keeping the division till here, at this point </p>

27 <p> <strong>Step 4 :</strong>The quotient obtained is the square root. In this case, it is 3.741…</p>

26 <p> <strong>Step 4 :</strong>The quotient obtained is the square root. In this case, it is 3.741…</p>

28 <h3>Square Root of 14 by Approximation Method</h3>

27 <h3>Square Root of 14 by Approximation Method</h3>

29 <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>

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

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

31 <p><strong>Step 1 :</strong>Identify the square roots of the perfect squares above and below 14</p>

30 <p><strong>Step 1 :</strong>Identify the square roots of the perfect squares above and below 14</p>

32 <p>Below : 9→ square root of 9 = 3 ……..(i)</p>

31 <p>Below : 9→ square root of 9 = 3 ……..(i)</p>

33 <p> Above : 16 →square root of 16= 4 ……..(ii)</p>

32 <p> Above : 16 →square root of 16= 4 ……..(ii)</p>

34 <p><strong>Step 2 :</strong>Divide 14 with one of 3 or 4</p>

33 <p><strong>Step 2 :</strong>Divide 14 with one of 3 or 4</p>

35 <p> If we choose 3, and divide 14 by 3, we get 4.666 …….(iii)</p>

34 <p> If we choose 3, and divide 14 by 3, we get 4.666 …….(iii)</p>

36 <p> <strong>Step 3:</strong>Find the<a>average</a>of 3 (from (i)) and 4.666 (from (iii))</p>

35 <p> <strong>Step 3:</strong>Find the<a>average</a>of 3 (from (i)) and 4.666 (from (iii))</p>

37 <p>(3+4.666)/2 = 3.833</p>

36 <p>(3+4.666)/2 = 3.833</p>

38 <p> Hence, 3.833 is the approximate square root of 14 </p>

37 <p> Hence, 3.833 is the approximate square root of 14 </p>

39 <h2>Common Mistakes and How to Avoid Them in the Square Root of 14</h2>

38 <h2>Common Mistakes and How to Avoid Them in the Square Root of 14</h2>

40 <p>When we find the square root of 14, 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>

39 <p>When we find the square root of 14, 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>

40 + <h2>Download Worksheets</h2>

41 <h3>Problem 1</h3>

42 <p>Simplify 7√14?</p>

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

44 <p>7√14</p>

45 <p>= 7⤬√14</p>

46 <p>= 7⤬3.741</p>

47 <p>= 26.187</p>

48 <p>Answer : 26.187 </p>

49 <h3>Explanation</h3>

50 <p>√14= 3.741, so multiplying the square root value with 7 </p>

51 <p>Well explained 👍</p>

52 <h3>Problem 2</h3>

53 <p>What is √14 + √11+ √14 ?</p>

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

55 <p>√14+ √11 + √14</p>

56 <p>= 3.741+3.316+3.741</p>

57 <p>= 10.798</p>

58 <p>Answer: 10.798 </p>

59 <h3>Explanation</h3>

60 <p> adding the square root value of 14 twice and adding the square root value of 11 with that. </p>

61 <p>Well explained 👍</p>

62 <h3>Problem 3</h3>

63 <p>Find the value of (1/√14)⤬ (1/√14) ?</p>

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

65 <p> (1/√14)⤬ (1/√14)</p>

66 <p>= 1/14</p>

67 <p>= 0.0741 </p>

68 <p>Answer: 0.0741 </p>

69 <h3>Explanation</h3>

70 <p> we know, √14⤬√14 = 14 and then solved by dividing 1 by 14</p>

71 <p>Well explained 👍</p>

72 <h3>Problem 4</h3>

73 <p>If y=√14, find (y²)²</p>

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

75 <p> firstly, y=√14</p>

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

77 <p>y2= (√14)2=14</p>

78 <p>Again, do the square of y2</p>

79 <p>(y2)2=(14)2= 196</p>

80 <p>Answer : 196 </p>

81 <h3>Explanation</h3>

82 <p>squaring “y” which is same as squaring the value of √14 resulted to 14. Again, squaring 14 resulted to 196. </p>

83 <p>Well explained 👍</p>

84 <h3>Problem 5</h3>

85 <p>Find √14 / √9</p>

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

87 <p> √14/√9</p>

88 <p>= √(14/9)</p>

89 <p>= 3.741/3</p>

90 <p>= 1.247</p>

91 <p>Answer : 1.247 </p>

92 <h3>Explanation</h3>

93 <p>dividing the square root value of 14 with that of square root value of 9.We conclude that, the square root of 14 is derived by multiplying 3.74165738677 with itself, i.e., 3.74165738677 ╳ 3.74165738677. The relation between square and square root is that they are inverse of each other. </p>

94 <p>Well explained 👍</p>

95 <h2>FAQs on 14 Square Root</h2>

96 <h3>1.How to solve √13 ?</h3>

97 <p>√13 can be solved by some methods to yield the square root value, namely, Long Division Method, Prime Factorization Method or Approximation Method. </p>

98 <h3>2.What is the cube root of 14 ?</h3>

99 <p>2.4101… is the<a>cube</a>root of 14. </p>

100 <h3>3.Is 14 a perfect square or non-perfect square?</h3>

101 <p>14 is a non-perfect square, since 14 =(3.74165738677) 2.</p>

102 <h3>4.Is the square root of 14 a rational or irrational number?</h3>

103 <p>The square root of 14 is ±3.74165738677. So, 3.74165738677 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>

104 <h3>5. What is the square of √14?</h3>

105 <h3>6.Is √14 a real number?</h3>

106 <h2>Important Glossaries for Square Root of 14</h2>

107 <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, 24 = 16, where 2 is the base, 4 is the exponent </li>

108 </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>

109 </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>

110 </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>

111 </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>

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

113 <p>▶</p>

114 <h2>Jaskaran Singh Saluja</h2>

115 <h3>About the Author</h3>

116 <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>

117 <h3>Fun Fact</h3>

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