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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 field of vehicle design, finance, etc. Here, we will discuss the square root of 676.</p>

4 <h2>What is the Square Root of 676?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 676 is a<a>perfect square</a>. The square root of 676 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √676, whereas (676)^(1/2) in the exponential form. √676 = 26, 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 676</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 676 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 676 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 676 Breaking it down, we get 2 x 2 x 13 x 13: 2^2 x 13^2</p>

14 <p><strong>Step 2:</strong>Now we found out the prime factors of 676. The second step is to make pairs of those prime factors. Since 676 is a perfect square, the digits of the number can be grouped in pairs.</p>

15 <p>Therefore, calculating √676 using prime factorization gives us 26.</p>

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18 <h2>Square Root of 676 by Long Division Method</h2>

17 <h2>Square Root of 676 by Long Division Method</h2>

19 <p>The<a>long division</a>method is particularly used for non-perfect square numbers, but it can also verify perfect squares. 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 particularly used for non-perfect square numbers, but it can also verify perfect squares. 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 676, we need to group it as 76 and 6.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 676, we need to group it as 76 and 6.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is 6. We can say n as ‘2’ because 2 x 2 = 4 is lesser than 6. Now the<a>quotient</a>is 2, after subtracting 6 - 4, the<a>remainder</a>is 2.</p>

20 <p><strong>Step 2:</strong>Now we need to find n whose square is 6. We can say n as ‘2’ because 2 x 2 = 4 is lesser than 6. Now the<a>quotient</a>is 2, after subtracting 6 - 4, the<a>remainder</a>is 2.</p>

22 <p><strong>Step 3:</strong>Now let us bring down 76, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2, we get 4, which will be our new divisor.</p>

21 <p><strong>Step 3:</strong>Now let us bring down 76, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 2 + 2, we get 4, which will be our new divisor.</p>

23 <p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.</p>

22 <p><strong>Step 4:</strong>The new divisor will be the<a>sum</a>of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.</p>

24 <p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 276. Let us consider n as 6, now 4 x 6 x 6 = 276.</p>

23 <p><strong>Step 5:</strong>The next step is finding 4n × n ≤ 276. Let us consider n as 6, now 4 x 6 x 6 = 276.</p>

25 <p><strong>Step 6:</strong>Subtract 276 from 276, the difference is 0, and the quotient is 26.</p>

24 <p><strong>Step 6:</strong>Subtract 276 from 276, the difference is 0, and the quotient is 26.</p>

26 <p>So the square root of √676 is 26.</p>

25 <p>So the square root of √676 is 26.</p>

27 <h2>Square Root of 676 by Approximation Method</h2>

26 <h2>Square Root of 676 by Approximation Method</h2>

28 <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 676 using the approximation method.</p>

27 <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 676 using the approximation method.</p>

29 <p><strong>Step 1:</strong>Now we have to find the closest perfect square of √676. Since 676 is a perfect square, it falls directly at 26.</p>

28 <p><strong>Step 1:</strong>Now we have to find the closest perfect square of √676. Since 676 is a perfect square, it falls directly at 26.</p>

30 <p><strong>Step 2:</strong>No further steps are needed as 676 is a perfect square, and its square root is already an integer.</p>

29 <p><strong>Step 2:</strong>No further steps are needed as 676 is a perfect square, and its square root is already an integer.</p>

31 <h2>Common Mistakes and How to Avoid Them in the Square Root of 676</h2>

30 <h2>Common Mistakes and How to Avoid Them in the Square Root of 676</h2>

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

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

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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 √576?</p>

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

36 <p>The area of the square is 576 square units.</p>

37 <h3>Explanation</h3>

38 <p>The area of the square = side².</p>

39 <p>The side length is given as √576.</p>

40 <p>Area of the square = side² = √576 x √576 = 24 x 24 = 576.</p>

41 <p>Therefore, the area of the square box is 576 square units.</p>

42 <p>Well explained 👍</p>

43 <h3>Problem 2</h3>

44 <p>A square-shaped building measuring 676 square feet is built; if each of the sides is √676, what will be the square feet of half of the building?</p>

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

46 <p>338 square feet</p>

47 <h3>Explanation</h3>

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

49 <p>Dividing 676 by 2 = we get 338.</p>

50 <p>So half of the building measures 338 square feet.</p>

51 <p>Well explained 👍</p>

52 <h3>Problem 3</h3>

53 <p>Calculate √676 x 5.</p>

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

55 <p>130</p>

56 <h3>Explanation</h3>

57 <p>The first step is to find the square root of 676, which is 26.</p>

58 <p>The second step is to multiply 26 with 5.</p>

59 <p>So 26 x 5 = 130.</p>

60 <p>Well explained 👍</p>

61 <h3>Problem 4</h3>

62 <p>What will be the square root of (400 + 276)?</p>

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

64 <p>The square root is 26.</p>

65 <h3>Explanation</h3>

66 <p>To find the square root, we need to find the sum of (400 + 276).</p>

67 <p>400 + 276 = 676, and then √676 = 26.</p>

68 <p>Therefore, the square root of (400 + 276) is ±26.</p>

69 <p>Well explained 👍</p>

70 <h3>Problem 5</h3>

71 <p>Find the perimeter of the rectangle if its length ‘l’ is √676 units and the width ‘w’ is 38 units.</p>

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

73 <p>We find the perimeter of the rectangle as 128 units.</p>

74 <h3>Explanation</h3>

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

76 <p>Perimeter = 2 × (√676 + 38)</p>

77 <p>= 2 × (26 + 38)</p>

78 <p>= 2 × 64</p>

79 <p>= 128 units.</p>

80 <p>Well explained 👍</p>

81 <h2>FAQ on Square Root of 676</h2>

82 <h3>1.What is √676 in its simplest form?</h3>

83 <p>The prime factorization of 676 is 2 x 2 x 13 x 13, so the simplest form of √676 = √(2 x 2 x 13 x 13) = 26.</p>

84 <h3>2.Mention the factors of 676.</h3>

85 <p>Factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, and 676.</p>

86 <h3>3.Calculate the square of 26.</h3>

87 <p>We get the square of 26 by multiplying the number by itself, that is 26 x 26 = 676.</p>

88 <h3>4.Is 676 a prime number?</h3>

89 <h3>5.676 is divisible by?</h3>

90 <p>676 has several factors; those are 1, 2, 4, 13, 26, 52, 169, 338, and 676.</p>

91 <h2>Important Glossaries for the Square Root of 676</h2>

92 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 5² = 25, and the inverse of the square is the square root, which is √25 = 5. </li>

93 <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>

94 <li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. For example, 676 is a perfect square because it is 26². </li>

95 <li><strong>Integer:</strong>An integer is a whole number that can be positive, negative, or zero. For example, -5, 0, and 3 are integers. </li>

96 <li><strong>Perimeter:</strong>The perimeter is the total distance around a two-dimensional shape.</li>

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

98 <p>▶</p>

99 <h2>Jaskaran Singh Saluja</h2>

100 <h3>About the Author</h3>

101 <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>

102 <h3>Fun Fact</h3>

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