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

3 <p>The square root of 29 is the inverse operation of squaring a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 29. 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 29?</h2>

5 <p>The<a>square</a>root<a>of</a>29 is ±5.38516480713.The positive value, 5.38516480713 is the solution of the<a>equation</a>x2 = 29. As defined, the square root is just the inverse of squaring a<a>number</a>, so, squaring 5.38516480713 will result in 29. The square root of 29 is expressed as √29 in radical form, where the ‘√’ sign is called “radical” sign. In<a>exponential form</a>, it is written as (29)1/2 </p>

6 <h2>Finding the Square Root of 29</h2>

7 <p>We can find the<a>square root</a>of 29 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 29 By Prime Factorization Method</h3>

12 <p>The<a>prime factorization</a>of 29 involves breaking down a number into its<a>factors</a>. Divide 29 by<a>prime numbers</a>, and continue to divide the quotients until they can’t be separated anymore. After factorizing 29, 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 29 = 29 × 1 </p>

14 <p> for 29, no pairs of factors are obtained, but a single 29 is obtained.</p>

15 <p>So, it can be expressed as √29 = √(29 × 1) = √29</p>

16 <p>√29 is the simplest radical form of √29</p>

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19 <h3>Square Root of 29 by Long Division Method</h3>

18 <h3>Square Root of 29 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 29:</p>

20 <p>Follow the steps to calculate the square root of 29:</p>

22 <p><strong>Step 1 :</strong>Write the number 29, and draw a bar above the pair of digits from right to left.</p>

21 <p><strong>Step 1 :</strong>Write the number 29, 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 29. Here, it is 5, Because 52=25 < 29</p>

22 <p> <strong>Step 2 :</strong>Now, find the greatest number whose square is<a>less than</a>or equal to 29. Here, it is 5, Because 52=25 < 29</p>

24 <p><strong>Step 3 :</strong>Now divide 29 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=3 is chosen such that when 3 is written beside the new divisor, 10, a 3-digit number is formed →103 and multiplying 3 with 103 gives 309 which is less than 400.</p>

23 <p><strong>Step 3 :</strong>Now divide 29 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=3 is chosen such that when 3 is written beside the new divisor, 10, a 3-digit number is formed →103 and multiplying 3 with 103 gives 309 which is less than 400.</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, 1775 (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, 1775 (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, is 5385…</p>

26 <p> <strong>Step 4 :</strong>The quotient obtained is the square root. In this case, is 5385…</p>

28 <h3>Square Root of 29 by Approximation Method</h3>

27 <h3>Square Root of 29 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 26</p>

30 <p><strong>Step 1 :</strong>Identify the square roots of the perfect squares above and below 26</p>

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

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

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

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

34 <p><strong>Step 2 :</strong>Divide 29 with one of 5 or 6.</p>

33 <p><strong>Step 2 :</strong>Divide 29 with one of 5 or 6.</p>

35 <p> If we choose 6, and divide 29 by 6, we get 4.833 …….(iii)</p>

34 <p> If we choose 6, and divide 29 by 6, we get 4.833 …….(iii)</p>

36 <p> <strong>Step 3:</strong>Find the<a>average</a>of 6 (from (ii)) and 4.833 (from (iii))</p>

35 <p> <strong>Step 3:</strong>Find the<a>average</a>of 6 (from (ii)) and 4.833 (from (iii))</p>

37 <p>(6+4.833)/2 = 5.4</p>

36 <p>(6+4.833)/2 = 5.4</p>

38 <p> Hence, 5.4 is the approximate square root of 29 </p>

37 <p> Hence, 5.4 is the approximate square root of 29 </p>

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

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

40 <p>When we find the square root of 26, 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 26, 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 15√29 (15√29+15√29)?</p>

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

44 <p>15√29 (15√29+15√29)</p>

45 <p>= 15√29(15√29⤬2)</p>

46 <p>=15√29(15⤬5.385⤬2)</p>

47 <p>=15√29(161.55)</p>

48 <p>= 15⤬5.385⤬161.55</p>

49 <p>= 13049.2012</p>

50 <p>Answer : 13049.2012 </p>

51 <h3>Explanation</h3>

52 <p> √29= 5.385, so multiplying the square root value with 15 in each part and then simplifying </p>

53 <p>Well explained 👍</p>

54 <h3>Problem 2</h3>

55 <p>What is (√29 +√30+√31) ?</p>

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

57 <p>29 +√30+√31</p>

58 <p>= 5.385 + 5.477 + 5.567</p>

59 <p>= 16.429</p>

60 <p>Answer: 16.429 </p>

61 <h3>Explanation</h3>

62 <p> adding the square root value of 29, square root value of 30 and square root value of 31 </p>

63 <p>Well explained 👍</p>

64 <h3>Problem 3</h3>

65 <p>Find :(√29 ⤬√29)/(√10⤬ √10)</p>

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

67 <p> (√29 ⤬√29)/(√10⤬ √10)</p>

68 <p>= 29/10</p>

69 <p>=2.9</p>

70 <p>Answer: 2.9 </p>

71 <h3>Explanation</h3>

72 <p>√29 ⤬√29 =29 and √10⤬ √10 =10. Using these, we divided the values </p>

73 <p>Well explained 👍</p>

74 <h3>Problem 4</h3>

75 <p>Find the difference between (√26)^2 - (√25)^2+ (√26)^2</p>

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

77 <p>(√26)2 - (√25)2+ (√26)2</p>

78 <p>= 26 -25+26</p>

79 <p>=27</p>

80 <p>Answer: 27 </p>

81 <h3>Explanation</h3>

82 <p>find out the square values of √26 and √25 and then simplified </p>

83 <p>Well explained 👍</p>

84 <h3>Problem 5</h3>

85 <p>Find (√29 / √16)⤬√29</p>

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

87 <p> (√29/√16)⤬√29</p>

88 <p>= √(29⤬29)/√16</p>

89 <p>= 29/4</p>

90 <p>= 7.25</p>

91 <p>Answer : 7.25 </p>

92 <h3>Explanation</h3>

93 <p>Since, √29⤬√29=29 so we simplified and divide by the √16 which is equal to 4 </p>

94 <p>Well explained 👍</p>

95 <h2>FAQs on 29 Square Root</h2>

96 <h3>1.How to solve √28?</h3>

97 <p>√28 can be solved through various methods like Long Division Method, Prime Factorization method or Approximation Method. The value of √28 is 5.2915… </p>

98 <h3>2.What is the cube root of 29 ?</h3>

99 <p>3.07231… is the<a>cube</a>root of 29. </p>

100 <h3>3.Is 29 a perfect square or non-perfect square?</h3>

101 <p> 29 is a non-perfect square, since 29 =( 5.38516480713)2. </p>

102 <h3>4.Is the square root of 29 a rational or irrational number?</h3>

103 <p>The square root of 29 is ± 5.38516480713. So, 5.38516480713 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.Is 28 a perfect square?</h3>

105 <p> No, 28 is not a perfect square since, (5.2915…)2=28 </p>

106 <h2>Important Glossaries for Square Root of 29</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>