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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 operation is finding the square root. The square root is used in various fields such as engineering, finance, and architecture. Here, we will discuss the square root of 726.</p>

4 <h2>What is the Square Root of 726?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>squaring a<a>number</a>. Since 726 is not a<a>perfect square</a>, its square root is expressed in both radical and exponential forms. In radical form, it is expressed as √726, whereas in<a>exponential form</a>, it is expressed as (726)^(1/2). √726 ≈ 26.933, which is an<a>irrational number</a>because it cannot be expressed as a<a>ratio</a>of two integers.</p>

6 <h2>Finding the Square Root of 726</h2>

7 <p>The<a>prime factorization</a>method is applicable for perfect square numbers. For non-perfect squares like 726, the<a>long division</a>and approximation methods are often used. Let's explore these 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 726 by Prime Factorization Method</h2>

12 <p>The prime factorization of a number involves expressing it as a<a>product</a>of<a>prime numbers</a>. Let's explore the prime factorization of 726.</p>

13 <p><strong>Step 1:</strong>Finding the prime<a>factors</a>of 726</p>

14 <p>Breaking it down, we get 2 x 3 x 11 x 11: 2^1 x 3^1 x 11^2</p>

15 <p><strong>Step 2:</strong>Now we have the prime factors of 726. Since 726 is not a perfect square, we cannot pair all the factors evenly. Thus, prime factorization doesn't yield an exact<a>square root</a>for 726.</p>

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18 <h2>Square Root of 726 by Long Division Method</h2>

17 <h2>Square Root of 726 by Long Division Method</h2>

19 <p>The long<a>division</a>method is used for non-perfect square numbers. Here's how to find the square root of 726 using this method:</p>

18 <p>The long<a>division</a>method is used for non-perfect square numbers. Here's how to find the square root of 726 using this method:</p>

20 <p><strong>Step 1:</strong>Group the digits of 726 from right to left. We group it as 26 and 7.</p>

19 <p><strong>Step 1:</strong>Group the digits of 726 from right to left. We group it as 26 and 7.</p>

21 <p><strong>Step 2:</strong>Find n whose square is closest to 7. Use n = 2 because 2 x 2 = 4, which is<a>less than</a>7. 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>Find n whose square is closest to 7. Use n = 2 because 2 x 2 = 4, which is<a>less than</a>7. 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>Bring down 26, making the new<a>dividend</a>326. Double the quotient (2), giving the new<a>divisor</a>as 4.</p>

21 <p><strong>Step 3:</strong>Bring down 26, making the new<a>dividend</a>326. Double the quotient (2), giving the new<a>divisor</a>as 4.</p>

23 <p><strong>Step 4:</strong>Find n such that (4n) x n ≤ 326. Let's use n = 7, giving us 47 x 7 = 329, which is too large, so let's try n = 6.</p>

22 <p><strong>Step 4:</strong>Find n such that (4n) x n ≤ 326. Let's use n = 7, giving us 47 x 7 = 329, which is too large, so let's try n = 6.</p>

24 <p><strong>Step 5:</strong>46 x 6 = 276. Subtract 276 from 326, leaving a remainder of 50.</p>

23 <p><strong>Step 5:</strong>46 x 6 = 276. Subtract 276 from 326, leaving a remainder of 50.</p>

25 <p><strong>Step 6:</strong>Add a<a>decimal</a>point and bring down two zeros, making it 5000. Use 532 x 3 = 1596, which is too large.</p>

24 <p><strong>Step 6:</strong>Add a<a>decimal</a>point and bring down two zeros, making it 5000. Use 532 x 3 = 1596, which is too large.</p>

26 <p><strong>Step 7:</strong>Adjust n to get a closer approximation. Continuously apply these steps until you reach the desired decimal precision.</p>

25 <p><strong>Step 7:</strong>Adjust n to get a closer approximation. Continuously apply these steps until you reach the desired decimal precision.</p>

27 <h2>Square Root of 726 by Approximation Method</h2>

26 <h2>Square Root of 726 by Approximation Method</h2>

28 <p>The approximation method is an easier way to estimate square roots:</p>

27 <p>The approximation method is an easier way to estimate square roots:</p>

29 <p><strong>Step 1:</strong>Identify the nearest perfect squares around 726. The nearest smaller perfect square is 625 (25^2), and the nearest larger is 729 (27^2). Thus, √726 is between 25 and 27.</p>

28 <p><strong>Step 1:</strong>Identify the nearest perfect squares around 726. The nearest smaller perfect square is 625 (25^2), and the nearest larger is 729 (27^2). Thus, √726 is between 25 and 27.</p>

30 <p><strong>Step 2:</strong>Use the<a>formula</a>for approximation: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) Using (726 - 625) / (729 - 625) = 101 / 104 ≈ 0.971. Adding this to the<a>base</a>of 25: 25 + 0.971 = 25.971, so the square root of 726 is approximately 25.971.</p>

29 <p><strong>Step 2:</strong>Use the<a>formula</a>for approximation: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) Using (726 - 625) / (729 - 625) = 101 / 104 ≈ 0.971. Adding this to the<a>base</a>of 25: 25 + 0.971 = 25.971, so the square root of 726 is approximately 25.971.</p>

31 <h2>Common Mistakes and How to Avoid Them in the Square Root of 726</h2>

30 <h2>Common Mistakes and How to Avoid Them in the Square Root of 726</h2>

32 <p>Students often make mistakes when calculating square roots, such as ignoring the negative square root or skipping steps in the long division method. Let's explore some common mistakes:</p>

31 <p>Students often make mistakes when calculating square roots, such as ignoring the negative square root or skipping steps in the long division method. Let's explore some common mistakes:</p>

32 + <h2>Download Worksheets</h2>

33 <h3>Problem 1</h3>

34 <p>Can you help Max find the area of a square box if its side length is given as √726?</p>

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

36 <p>The area of the square is approximately 726 square units.</p>

37 <h3>Explanation</h3>

38 <p>The area of a square is calculated as side^2.</p>

39 <p>With a side length of √726, the area = (√726)^2 = 726 square units.</p>

40 <p>Well explained 👍</p>

41 <h3>Problem 2</h3>

42 <p>A square-shaped building measures 726 square feet. If each side is √726, what will be the square footage of half the building?</p>

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

44 <p>363 square feet</p>

45 <h3>Explanation</h3>

46 <p>Since the building is square-shaped, dividing the total area by 2 gives half the building's area: 726 / 2 = 363 square feet.</p>

47 <p>Well explained 👍</p>

48 <h3>Problem 3</h3>

49 <p>Calculate √726 x 5.</p>

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

51 <p>Approximately 134.665</p>

52 <h3>Explanation</h3>

53 <p>First, find the square root of 726, approximately 26.933, then multiply by 5: 26.933 x 5 = 134.665.</p>

54 <p>Well explained 👍</p>

55 <h3>Problem 4</h3>

56 <p>What will be the square root of (726 + 9)?</p>

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

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

59 <h3>Explanation</h3>

60 <p>Calculate the sum of (726 + 9) = 735, then find the square root: √735 ≈ 27.</p>

61 <p>Well explained 👍</p>

62 <h3>Problem 5</h3>

63 <p>Find the perimeter of the rectangle if its length ‘l’ is √726 units and the width ‘w’ is 20 units.</p>

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

65 <p>The perimeter is approximately 93.866 units.</p>

66 <h3>Explanation</h3>

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

68 <p>Perimeter = 2 × (√726 + 20) ≈ 2 × (26.933 + 20) ≈ 2 × 46.933 = 93.866 units.</p>

69 <p>Well explained 👍</p>

70 <h2>FAQ on Square Root of 726</h2>

71 <h3>1.What is √726 in its simplest form?</h3>

72 <p>The prime factorization of 726 is 2 x 3 x 11 x 11, so the simplest form of √726 is √(2 x 3 x 11^2).</p>

73 <h3>2.Mention the factors of 726.</h3>

74 <p>Factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, and 726.</p>

75 <h3>3.Calculate the square of 726.</h3>

76 <p>The square of 726 is obtained by multiplying it by itself: 726 x 726 = 527076.</p>

77 <h3>4.Is 726 a prime number?</h3>

78 <p>No, 726 is not a prime number because it has more than two factors.</p>

79 <h3>5.726 is divisible by?</h3>

80 <p>726 is divisible by 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, and 726.</p>

81 <h2>Important Glossaries for the Square Root of 726</h2>

82 <ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. For example, 5^2 = 25, so √25 = 5.</li>

83 </ul><ul><li><strong>Irrational number:</strong>An irrational number cannot be expressed as a simple fraction. For instance, √726 is irrational.</li>

84 </ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that has an integer as its square root, such as 25, whose square root is 5.</li>

85 </ul><ul><li><strong>Prime factorization:</strong>Expressing a number as a product of prime numbers, e.g., 726 = 2 x 3 x 11 x 11.</li>

86 </ul><ul><li><strong>Long division method:</strong>A step-by-step technique to find the square root of non-perfect squares.</li>

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

88 <p>▶</p>

89 <h2>Jaskaran Singh Saluja</h2>

90 <h3>About the Author</h3>

91 <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>

92 <h3>Fun Fact</h3>

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