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

3 <p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the fields of vehicle design, finance, etc. Here, we will discuss the square root of 729.</p>

4 <h2>What is the Square Root of 729?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 729 is a<a>perfect square</a>. The square root of 729 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √729, whereas (729)^(1/2) in the exponential form. √729 = 27, which is a<a>rational number</a>because it can 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 729</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers like 729. The long-<a>division</a>method and approximation method can also be used but are not necessary. 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 729 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 729 is broken down into its prime factors.</p>

13 <p><strong>Step 1</strong>: Finding the prime factors of 729</p>

14 <p>Breaking it down, we get 3 x 3 x 3 x 3 x 3 x 3: 3^6</p>

15 <p><strong>Step 2:</strong>Now we found out the prime factors of 729. The second step is to make pairs of those prime factors. Since 729 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating √729 using prime factorization is possible, and we get 3^3 = 27.</p>

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18 <h2>Square Root of 729 by Long Division Method</h2>

17 <h2>Square Root of 729 by Long Division Method</h2>

19 <p>The<a>long division</a>method is useful for verifying square roots. In this method, we should check the closest perfect square number for 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 useful for verifying square roots. In this method, we should check the closest perfect square number for 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>To begin with, we need to group the numbers from right to left. In the case of 729, we need to group it as 29 and 7.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 729, we need to group it as 29 and 7.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is 7. We can say n as ‘2’ because 2 x 2 is<a>less than</a>or equal to 7. Now the<a>quotient</a>is 2, and after subtracting 4 from 7, the<a>remainder</a>is 3.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is 7. We can say n as ‘2’ because 2 x 2 is<a>less than</a>or equal to 7. Now the<a>quotient</a>is 2, and after subtracting 4 from 7, the<a>remainder</a>is 3.</p>

22 <p><strong>Step 3:</strong>Now bring down 29, making the new<a>dividend</a>329. Add the old<a>divisor</a>with the quotient, 2 + 2 = 4, which will be our new divisor.</p>

21 <p><strong>Step 3:</strong>Now bring down 29, making the new<a>dividend</a>329. Add the old<a>divisor</a>with the quotient, 2 + 2 = 4, which will be our new divisor.</p>

23 <p><strong>Step 4:</strong>The new divisor will be 4n. We need to find the value of n such that 4n x n ≤ 329. Let us consider n as 7; now 47 x 7 = 329. Step 5: Subtract 329 from 329; the difference is 0, and the quotient is 27.</p>

22 <p><strong>Step 4:</strong>The new divisor will be 4n. We need to find the value of n such that 4n x n ≤ 329. Let us consider n as 7; now 47 x 7 = 329. Step 5: Subtract 329 from 329; the difference is 0, and the quotient is 27.</p>

24 <p>So the square root of √729 is 27.</p>

23 <p>So the square root of √729 is 27.</p>

25 <h2>Square Root of 729 by Approximation Method</h2>

24 <h2>Square Root of 729 by Approximation Method</h2>

26 <p>The approximation method can be used to verify the square roots, but it is not necessary for perfect squares like 729. We can directly find the square root of 729 as 27 using the prime factorization or long division method.</p>

25 <p>The approximation method can be used to verify the square roots, but it is not necessary for perfect squares like 729. We can directly find the square root of 729 as 27 using the prime factorization or long division method.</p>

27 <h2>Common Mistakes and How to Avoid Them in the Square Root of 729</h2>

26 <h2>Common Mistakes and How to Avoid Them in the Square Root of 729</h2>

28 <p>Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of those mistakes that students tend to make in detail.</p>

27 <p>Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of those mistakes that students tend to make in detail.</p>

28 + <h2>Download Worksheets</h2>

29 <h3>Problem 1</h3>

30 <p>Can you help Max find the area of a square box if its side length is given as √729?</p>

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

32 <p>The area of the square is 729 square units.</p>

33 <h3>Explanation</h3>

34 <p>The area of the square = side^2.</p>

35 <p>The side length is given as √729.</p>

36 <p>Area of the square = side^2 = √729 x √729 = 27 x 27 = 729.</p>

37 <p>Therefore, the area of the square box is 729 square units.</p>

38 <p>Well explained 👍</p>

39 <h3>Problem 2</h3>

40 <p>A square-shaped building measuring 729 square feet is built; if each of the sides is √729, what will be the square feet of half of the building?</p>

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

42 <p>364.5 square feet</p>

43 <h3>Explanation</h3>

44 <p>We can just divide the given area by 2 as the building is square-shaped.</p>

45 <p>Dividing 729 by 2, we get 364.5.</p>

46 <p>So half of the building measures 364.5 square feet.</p>

47 <p>Well explained 👍</p>

48 <h3>Problem 3</h3>

49 <p>Calculate √729 x 5.</p>

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

51 <p>135</p>

52 <h3>Explanation</h3>

53 <p>The first step is to find the square root of 729, which is 27.</p>

54 <p>The second step is to multiply 27 with 5.</p>

55 <p>So 27 x 5 = 135.</p>

56 <p>Well explained 👍</p>

57 <h3>Problem 4</h3>

58 <p>What will be the square root of (625 + 104)?</p>

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

60 <p>The square root is 27.</p>

61 <h3>Explanation</h3>

62 <p>To find the square root, we need to find the sum of (625 + 104). 625 + 104 = 729, and then √729 = 27.</p>

63 <p>Therefore, the square root of (625 + 104) is ±27.</p>

64 <p>Well explained 👍</p>

65 <h3>Problem 5</h3>

66 <p>Find the perimeter of the rectangle if its length ‘l’ is √729 units and the width ‘w’ is 10 units.</p>

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

68 <p>We find the perimeter of the rectangle as 74 units.</p>

69 <h3>Explanation</h3>

70 <p>Perimeter of the rectangle = 2 × (length + width).</p>

71 <p>Perimeter = 2 × (√729 + 10) = 2 × (27 + 10) = 2 × 37 = 74 units.</p>

72 <p>Well explained 👍</p>

73 <h2>FAQ on Square Root of 729</h2>

74 <h3>1.What is √729 in its simplest form?</h3>

75 <p>The prime factorization of 729 is 3 x 3 x 3 x 3 x 3 x 3, so the simplest form of √729 = 3^3 = 27.</p>

76 <h3>2.Mention the factors of 729.</h3>

77 <p>Factors of 729 are 1, 3, 9, 27, 81, 243, and 729.</p>

78 <h3>3.Calculate the square of 729.</h3>

79 <p>We get the square of 729 by multiplying the number by itself, that is 729 x 729 = 531441.</p>

80 <h3>4.Is 729 a prime number?</h3>

81 <h3>5.729 is divisible by?</h3>

82 <p>729 has several factors; those are 1, 3, 9, 27, 81, 243, and 729.</p>

83 <h2>Important Glossaries for the Square Root of 729</h2>

84 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 6^2 = 36, and the inverse of the square is the square root that is √36 = 6.</li>

85 </ul><ul><li><strong>Rational number:</strong>A rational number is a number that can be written in the form of p/q, where q is not equal to zero, and p and q are integers.</li>

86 </ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. For example, 729 is a perfect square because it is 27^2.</li>

87 </ul><ul><li><strong>Prime factorization:</strong>Breaking down a number into its prime factors. For example, the prime factorization of 729 is 3 x 3 x 3 x 3 x 3 x 3.</li>

88 </ul><ul><li><strong>Perimeter:</strong>The perimeter is the distance around a two-dimensional shape. For example, the perimeter of a rectangle is 2 × (length + width).</li>

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

90 <p>▶</p>

91 <h2>Jaskaran Singh Saluja</h2>

92 <h3>About the Author</h3>

93 <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>

94 <h3>Fun Fact</h3>

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