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

3 <p>If a number is multiplied by itself, 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, finance, etc. Here, we will discuss the square root of 1729.</p>

4 <h2>What is the Square Root of 1729?</h2>

5 <p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 1729 is not a<a>perfect square</a>. The square root of 1729 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √1729, whereas in exponential form it is (1729)^(1/2). √1729 ≈ 41.5633, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>

6 <h2>Finding the Square Root of 1729</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the long-<a>division</a>method and approximation method are used. Let us now learn the following methods:</p>

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

9 <li>Long division method</li>

10 <li>Approximation method</li>

11 </ul><h2>Square Root of 1729 by Prime Factorization Method</h2>

12 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 1729 is broken down into its prime factors:</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 1729 Breaking it down, we get 7 x 13 x 19.</p>

14 <p><strong>Step 2:</strong>Now we found out the prime factors of 1729. The second step is to make pairs of those prime factors. Since 1729 is not a perfect square, the digits of the number cannot be grouped in pairs.</p>

15 <p>Therefore, calculating √1729 using prime factorization is not straightforward.</p>

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18 <h2>Square Root of 1729 by Long Division Method</h2>

17 <h2>Square Root of 1729 by Long Division Method</h2>

19 <p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we check the closest perfect square number to the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step:</p>

18 <p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we check the closest perfect square number to the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step:</p>

20 <p><strong>Step 1:</strong>Group the numbers from right to left. In the case of 1729, group it as 17 and 29.</p>

19 <p><strong>Step 1:</strong>Group the numbers from right to left. In the case of 1729, group it as 17 and 29.</p>

21 <p><strong>Step 2:</strong>Find a number whose square is<a>less than</a>or equal to 17. This number is 4, since 4 x 4 = 16. The<a>quotient</a>is 4, and the<a>remainder</a>is 1 (17 - 16).</p>

20 <p><strong>Step 2:</strong>Find a number whose square is<a>less than</a>or equal to 17. This number is 4, since 4 x 4 = 16. The<a>quotient</a>is 4, and the<a>remainder</a>is 1 (17 - 16).</p>

22 <p><strong>Step 3:</strong>Bring down the next pair, 29, to get the new<a>dividend</a>, 129.</p>

21 <p><strong>Step 3:</strong>Bring down the next pair, 29, to get the new<a>dividend</a>, 129.</p>

23 <p><strong>Step 4:</strong>Double the previous quotient (4) to get 8, which will be part of the new<a>divisor</a>.</p>

22 <p><strong>Step 4:</strong>Double the previous quotient (4) to get 8, which will be part of the new<a>divisor</a>.</p>

24 <p><strong>Step 5:</strong>Find a number n such that 8n x n is less than or equal to 129. In this case, n is 1, since 81 x 1 = 81.</p>

23 <p><strong>Step 5:</strong>Find a number n such that 8n x n is less than or equal to 129. In this case, n is 1, since 81 x 1 = 81.</p>

25 <p><strong>Step 6:</strong>Subtract 81 from 129 to get a remainder of 48, and the quotient is 41.</p>

24 <p><strong>Step 6:</strong>Subtract 81 from 129 to get a remainder of 48, and the quotient is 41.</p>

26 <p><strong>Step 7:</strong>Add decimal points to the quotient and bring down pairs of zeros.</p>

25 <p><strong>Step 7:</strong>Add decimal points to the quotient and bring down pairs of zeros.</p>

27 <p><strong>Step 8</strong>: Repeat the process to find the next digit(s) after the decimal point.</p>

26 <p><strong>Step 8</strong>: Repeat the process to find the next digit(s) after the decimal point.</p>

28 <p>The square root of 1729 is approximately 41.563.</p>

27 <p>The square root of 1729 is approximately 41.563.</p>

29 <h2>Square Root of 1729 by Approximation Method</h2>

28 <h2>Square Root of 1729 by Approximation Method</h2>

30 <p>The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 1729 using the approximation method.</p>

29 <p>The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 1729 using the approximation method.</p>

31 <p><strong>Step 1:</strong>Find the closest perfect squares around 1729.</p>

30 <p><strong>Step 1:</strong>Find the closest perfect squares around 1729.</p>

32 <p>The smallest is 1600 (40^2) and the largest is 1764 (42^2).</p>

31 <p>The smallest is 1600 (40^2) and the largest is 1764 (42^2).</p>

33 <p>√1729 falls somewhere between 40 and 42.</p>

32 <p>√1729 falls somewhere between 40 and 42.</p>

34 <p><strong>Step 2:</strong>Apply the<a>formula</a>:</p>

33 <p><strong>Step 2:</strong>Apply the<a>formula</a>:</p>

35 <p>(Given number - smaller perfect square) / (larger perfect square - smaller perfect square).</p>

34 <p>(Given number - smaller perfect square) / (larger perfect square - smaller perfect square).</p>

36 <p>(1729 - 1600) / (1764 - 1600) = 129 / 164 ≈ 0.786.</p>

35 <p>(1729 - 1600) / (1764 - 1600) = 129 / 164 ≈ 0.786.</p>

37 <p><strong>Step 3:</strong>Add this<a>decimal</a>to the smaller square root: 40 + 0.786 = 40.786.</p>

36 <p><strong>Step 3:</strong>Add this<a>decimal</a>to the smaller square root: 40 + 0.786 = 40.786.</p>

38 <p>The square root of 1729 is approximately 41.563, refining the approximation from the previous steps.</p>

37 <p>The square root of 1729 is approximately 41.563, refining the approximation from the previous steps.</p>

39 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1729</h2>

38 <h2>Common Mistakes and How to Avoid Them in the Square Root of 1729</h2>

40 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of these mistakes in detail.</p>

39 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of these mistakes in detail.</p>

40 + <h2>Download Worksheets</h2>

41 <h3>Problem 1</h3>

42 <p>Can you help Max find the area of a square box if its side length is given as √1729?</p>

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

44 <p>The area of the square is 1729 square units.</p>

45 <h3>Explanation</h3>

46 <p>The area of the square = side^2. The side length is given as √1729. Area of the square = side^2 = √1729 x √1729 = 1729. Therefore, the area of the square box is 1729 square units.</p>

47 <p>Well explained 👍</p>

48 <h3>Problem 2</h3>

49 <p>A square-shaped building measuring 1729 square feet is built; if each of the sides is √1729, what will be the square feet of half of the building?</p>

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

51 <p>864.5 square feet</p>

52 <h3>Explanation</h3>

53 <p>We can divide the given area by 2 as the building is square-shaped. Dividing 1729 by 2, we get 864.5. So half of the building measures 864.5 square feet.</p>

54 <p>Well explained 👍</p>

55 <h3>Problem 3</h3>

56 <p>Calculate √1729 x 5.</p>

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

58 <p>207.8165</p>

59 <h3>Explanation</h3>

60 <p>The first step is to find the square root of 1729, which is approximately 41.563, and then multiply by 5. So, 41.563 x 5 ≈ 207.8165.</p>

61 <p>Well explained 👍</p>

62 <h3>Problem 4</h3>

63 <p>What will be the square root of (1600 + 129)?</p>

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

65 <p>The square root is approximately 41.563.</p>

66 <h3>Explanation</h3>

67 <p>To find the square root, find the sum of (1600 + 129) = 1729, then √1729 ≈ 41.563. Therefore, the square root of (1600 + 129) is approximately ±41.563.</p>

68 <p>Well explained 👍</p>

69 <h3>Problem 5</h3>

70 <p>Find the perimeter of the rectangle if its length ‘l’ is √1729 units and the width ‘w’ is 38 units.</p>

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

72 <p>The perimeter of the rectangle is approximately 159.126 units.</p>

73 <h3>Explanation</h3>

74 <p>Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√1729 + 38) ≈ 2 × (41.563 + 38) = 2 × 79.563 ≈ 159.126 units.</p>

75 <p>Well explained 👍</p>

76 <h2>FAQ on Square Root of 1729</h2>

77 <h3>1.What is √1729 in its simplest form?</h3>

78 <p>The prime factorization of 1729 is 7 x 13 x 19, so the simplest form of √1729 is √(7 x 13 x 19).</p>

79 <h3>2.Mention the factors of 1729.</h3>

80 <p>Factors of 1729 are 1, 7, 13, 19, 91, 133, 247, and 1729.</p>

81 <h3>3.Calculate the square of 1729.</h3>

82 <p>We get the square of 1729 by multiplying the number by itself, that is 1729 x 1729 = 2,990,041.</p>

83 <h3>4.Is 1729 a prime number?</h3>

84 <p>1729 is not a<a>prime number</a>, as it has more than two factors.</p>

85 <h3>5.1729 is divisible by?</h3>

86 <p>1729 has several factors; those are 1, 7, 13, 19, 91, 133, 247, and 1729.</p>

87 <h2>Important Glossaries for the Square Root of 1729</h2>

88 <ul><li><strong>Square root:</strong>A square root is the inverse operation to squaring a number. Example: 4^2 = 16, and the inverse of squaring is the square root, so √16 = 4. </li>

89 <li><strong>Irrational number:</strong>An irrational number is a number that cannot be written as a simple fraction (p/q), where p and q are integers and q is not zero. </li>

90 <li><strong>Approximation:</strong>The process of finding a value that is close enough to the right answer, typically with some thought or calculation involved. </li>

91 <li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 4, 9, and 16 are perfect squares. </li>

92 <li><strong>Long division method:</strong>A method used to find the square root of a number by performing division and averaging processes iteratively.</li>

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

94 <p>▶</p>

95 <h2>Jaskaran Singh Saluja</h2>

96 <h3>About the Author</h3>

97 <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>

98 <h3>Fun Fact</h3>

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