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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 7744.</p>

4 <h2>What is the Square Root of 7744?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 7744 is a<a>perfect square</a>. The square root of 7744 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √7744, whereas (7744)^(1/2) in the exponential form. √7744 = 88, 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 7744</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, the<a>long division</a>method can also be used for any number. Let us now learn the following methods:</p>

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

9 <li>Long division method</li>

10 </ul><h2>Square Root of 7744 by Prime Factorization Method</h2>

11 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 7744 is broken down into its prime factors.</p>

12 <p><strong>Step 1:</strong>Finding the prime factors of 7744 Breaking it down, we get 2 x 2 x 2 x 2 x 11 x 11: 2^4 x 11^2</p>

13 <p><strong>Step 2:</strong>Now we found out the prime factors of 7744. The second step is to make pairs of those prime factors. Since 7744 is a perfect square, we can pair the digits: (2 x 2) x (2 x 2) x (11 x 11).</p>

14 <p><strong>Step 3:</strong>Taking one factor from each pair gives us the<a>square root</a>: 2 x 2 x 11 = 44.</p>

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17 <h2>Square Root of 7744 by Long Division Method</h2>

16 <h2>Square Root of 7744 by Long Division Method</h2>

18 <p>The long<a>division</a>method is particularly used for non-perfect square numbers, but it can also be used for perfect squares. Let us now learn how to find the square root using the long division method, step by step.</p>

17 <p>The long<a>division</a>method is particularly used for non-perfect square numbers, but it can also be used for perfect squares. Let us now learn how to find the square root using the long division method, step by step.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 7744, we group it as 77 and 44.</p>

18 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 7744, we group it as 77 and 44.</p>

20 <p><strong>Step 2:</strong>Now we need to find a number whose square is<a>less than</a>or equal to 77. We can use 8 since 8 x 8 = 64. Subtracting 64 from 77 gives us 13.</p>

19 <p><strong>Step 2:</strong>Now we need to find a number whose square is<a>less than</a>or equal to 77. We can use 8 since 8 x 8 = 64. Subtracting 64 from 77 gives us 13.</p>

21 <p><strong>Step 3:</strong>Bring down the next pair, 44, making the new<a>dividend</a>1344. Add the old<a>divisor</a>with the same number: 8 + 8 = 16, which will be our new divisor.</p>

20 <p><strong>Step 3:</strong>Bring down the next pair, 44, making the new<a>dividend</a>1344. Add the old<a>divisor</a>with the same number: 8 + 8 = 16, which will be our new divisor.</p>

22 <p><strong>Step 4:</strong>The new divisor will be 160. Find a number n such that (160 + n) x n ≤ 1344. We find n = 8 since 168 x 8 = 1344.</p>

21 <p><strong>Step 4:</strong>The new divisor will be 160. Find a number n such that (160 + n) x n ≤ 1344. We find n = 8 since 168 x 8 = 1344.</p>

23 <p><strong>Step 5:</strong>Subtracting 1344 from 1344 gives 0. So we have found the square root to be 88.</p>

22 <p><strong>Step 5:</strong>Subtracting 1344 from 1344 gives 0. So we have found the square root to be 88.</p>

24 <h2>Common Mistakes and How to Avoid Them in the Square Root of 7744</h2>

23 <h2>Common Mistakes and How to Avoid Them in the Square Root of 7744</h2>

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

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

26 <h2>Common Mistakes and How to Avoid Them in the Square Root of 7744</h2>

25 <h2>Common Mistakes and How to Avoid Them in the Square Root of 7744</h2>

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

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

27 + <h2>Download Worksheets</h2>

28 <h3>Problem 1</h3>

29 <p>Can you help Max find the area of a square box if its side length is given as √7744?</p>

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

31 <p>The area of the square is 7744 square units.</p>

32 <h3>Explanation</h3>

33 <p>The area of the square = side^2. The side length is given as √7744. Area of the square = side^2 = √7744 x √7744 = 88 x 88 = 7744. Therefore, the area of the square box is 7744 square units.</p>

34 <p>Well explained 👍</p>

35 <h3>Problem 2</h3>

36 <p>A square-shaped building measuring 7744 square feet is built; if each of the sides is √7744, what will be the square feet of half of the building?</p>

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

38 <p>3872 square feet</p>

39 <h3>Explanation</h3>

40 <p>We can just divide the given area by 2 as the building is square-shaped. Dividing 7744 by 2, we get 3872. So half of the building measures 3872 square feet.</p>

41 <p>Well explained 👍</p>

42 <h3>Problem 3</h3>

43 <p>Calculate √7744 x 5.</p>

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

45 <p>440</p>

46 <h3>Explanation</h3>

47 <p>The first step is to find the square root of 7744, which is 88. The second step is to multiply 88 by 5. So, 88 x 5 = 440.</p>

48 <p>Well explained 👍</p>

49 <h3>Problem 4</h3>

50 <p>What will be the square root of (7744 + 256)?</p>

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

52 <p>The square root is 92.</p>

53 <h3>Explanation</h3>

54 <p>To find the square root, we need to find the sum of (7744 + 256). 7744 + 256 = 8000. The square root of 8000 is 89.44, which can be approximated to 92 when rounded.</p>

55 <p>Well explained 👍</p>

56 <h3>Problem 5</h3>

57 <p>Find the perimeter of the rectangle if its length ‘l’ is √7744 units and the width ‘w’ is 88 units.</p>

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

59 <p>352 units</p>

60 <h3>Explanation</h3>

61 <p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√7744 + 88) = 2 × (88 + 88) = 2 × 176 = 352 units.</p>

62 <p>Well explained 👍</p>

63 <h2>FAQ on Square Root of 7744</h2>

64 <h3>1.What is √7744 in its simplest form?</h3>

65 <p>The prime factorization of 7744 is 2 x 2 x 2 x 2 x 11 x 11, so the simplest form of √7744 is 88.</p>

66 <h3>2.Mention the factors of 7744.</h3>

67 <p>Factors of 7744 include 1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 484, 968, 1936, 3872, and 7744.</p>

68 <h3>3.Calculate the square of 88.</h3>

69 <p>We get the square of 88 by multiplying the number by itself, that is 88 x 88 = 7744.</p>

70 <h3>4.Is 7744 a perfect square?</h3>

71 <p>Yes, 7744 is a perfect square, as it can be expressed as 88 squared.</p>

72 <h3>5.7744 is divisible by?</h3>

73 <p>7744 is divisible by its factors: 1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 484, 968, 1936, 3872, and 7744.</p>

74 <h2>Important Glossaries for the Square Root of 7744</h2>

75 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. For example, 88^2 = 7744, and the inverse of the square is the square root, which is √7744 = 88. </li>

76 <li><strong>Perfect square:</strong>A perfect square is an integer that is the square of an integer. For example, 7744 is a perfect square because it is 88 squared. </li>

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

78 <li><strong>Principal square root:</strong>A number has both positive and negative square roots, but the positive square root is often used in practical applications. This is known as the principal square root. </li>

79 <li><strong>Prime factorization:</strong>Prime factorization is expressing a number as the product of its prime factors. For example, the prime factorization of 7744 is 2^4 x 11^2.</li>

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

81 <p>▶</p>

82 <h2>Jaskaran Singh Saluja</h2>

83 <h3>About the Author</h3>

84 <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>

85 <h3>Fun Fact</h3>

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