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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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 9801.</p>

4 <h2>What is the Square Root of 9801?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 9801 is a<a>perfect square</a>. The square root of 9801 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √9801, whereas (9801)^(1/2) in the exponential form. √9801 = 99, 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 9801</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. Here, we will use the prime factorization method to find the<a>square root</a>of 9801.</p>

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

9 </ul><h2>Square Root of 9801 by Prime Factorization Method</h2>

10 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 9801 is broken down into its prime factors.</p>

11 <p><strong>Step 1:</strong>Finding the prime factors of 9801</p>

12 <p>Breaking it down, we get 3 × 3 × 1089, and 1089 = 3 × 3 × 121, and 121 = 11 × 11. Thus, 9801 = 3 × 3 × 3 × 3 × 11 × 11.</p>

13 <p><strong>Step 2:</strong>Now we found out the prime factors of 9801. The next step is to make pairs of those prime factors: (3, 3), (3, 3), and (11, 11). Since 9801 is a perfect square, we can pair the factors. Therefore, calculating 9801 using prime factorization, we get √9801 = 3 × 3 × 11 = 99.</p>

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16 <h2>Square Root of 9801 by Long Division Method</h2>

15 <h2>Square Root of 9801 by Long Division Method</h2>

17 <p>The<a>long division</a>method is particularly used for non-perfect square numbers. However, it can also be applied to perfect squares for verification. Here is how you can find the square root using the long division method:</p>

16 <p>The<a>long division</a>method is particularly used for non-perfect square numbers. However, it can also be applied to perfect squares for verification. Here is how you can find the square root using the long division method:</p>

18 <p><strong>Step 1:</strong>Pair the digits of 9801 starting from the right: 98 and 01.</p>

17 <p><strong>Step 1:</strong>Pair the digits of 9801 starting from the right: 98 and 01.</p>

19 <p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to 98. Here, it is 9, as 9 × 9 = 81.</p>

18 <p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to 98. Here, it is 9, as 9 × 9 = 81.</p>

20 <p><strong>Step 3:</strong>Subtract 81 from 98 to get the<a>remainder</a>17. Bring down the next pair, 01, to get 1701.</p>

19 <p><strong>Step 3:</strong>Subtract 81 from 98 to get the<a>remainder</a>17. Bring down the next pair, 01, to get 1701.</p>

21 <p><strong>Step 4:</strong>Double the<a>quotient</a>obtained so far (9) to get 18, and find a digit n such that 18n × n ≤ 1701.</p>

20 <p><strong>Step 4:</strong>Double the<a>quotient</a>obtained so far (9) to get 18, and find a digit n such that 18n × n ≤ 1701.</p>

22 <p><strong>Step 5:</strong>n is 9 here, since 189 × 9 = 1701.</p>

21 <p><strong>Step 5:</strong>n is 9 here, since 189 × 9 = 1701.</p>

23 <p><strong>Step 6:</strong>Subtracting 1701 from 1701 leaves a remainder of 0. The quotient obtained is 99.</p>

22 <p><strong>Step 6:</strong>Subtracting 1701 from 1701 leaves a remainder of 0. The quotient obtained is 99.</p>

24 <p>So, the square root of √9801 is 99.</p>

23 <p>So, the square root of √9801 is 99.</p>

25 <h2>Square Root of 9801 by Approximation Method</h2>

24 <h2>Square Root of 9801 by Approximation Method</h2>

26 <p>Since 9801 is a perfect square, the approximation method is not needed. However, if it were not, this method could be useful for finding square roots to a certain degree of<a>accuracy</a>.</p>

25 <p>Since 9801 is a perfect square, the approximation method is not needed. However, if it were not, this method could be useful for finding square roots to a certain degree of<a>accuracy</a>.</p>

27 <p><strong>Step 1:</strong>Identify the perfect squares closest to 9801. The closest are 9604 (98^2) and 10000 (100^2). Since 9801 is exactly 99^2, the approximation method confirms the exactness.</p>

26 <p><strong>Step 1:</strong>Identify the perfect squares closest to 9801. The closest are 9604 (98^2) and 10000 (100^2). Since 9801 is exactly 99^2, the approximation method confirms the exactness.</p>

28 <h2>Common Mistakes and How to Avoid Them in the Square Root of 9801</h2>

27 <h2>Common Mistakes and How to Avoid Them in the Square Root of 9801</h2>

29 <p>Students make mistakes while finding the square root, such as forgetting about the negative square root and 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 <p>Students make mistakes while finding the square root, such as forgetting about the negative square root and 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>

29 + <h2>Download Worksheets</h2>

30 <h3>Problem 1</h3>

31 <p>Can you help Max find the side length of a square if its area is given as 9801 square units?</p>

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

33 <p>The side length of the square is 99 units.</p>

34 <h3>Explanation</h3>

35 <p>The side length of the square = √area.</p>

36 <p>The area is given as 9801 square units.</p>

37 <p>Side length = √9801 = 99.</p>

38 <p>Therefore, the side length of the square is 99 units.</p>

39 <p>Well explained 👍</p>

40 <h3>Problem 2</h3>

41 <p>A square-shaped garden measuring 9801 square feet is built. If each of the sides is √9801, what will be the square feet of half of the garden?</p>

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

43 <p>4900.5 square feet</p>

44 <h3>Explanation</h3>

45 <p>We can divide the given area by 2 as the garden is square-shaped.</p>

46 <p>Dividing 9801 by 2, we get 4900.5.</p>

47 <p>So half of the garden measures 4900.5 square feet.</p>

48 <p>Well explained 👍</p>

49 <h3>Problem 3</h3>

50 <p>Calculate √9801 × 5.</p>

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

52 <p>495</p>

53 <h3>Explanation</h3>

54 <p>The first step is to find the square root of 9801, which is 99.</p>

55 <p>The second step is to multiply 99 with 5.</p>

56 <p>So, 99 × 5 = 495.</p>

57 <p>Well explained 👍</p>

58 <h3>Problem 4</h3>

59 <p>What will be the square root of (9801 + 0)?</p>

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

61 <p>The square root is 99.</p>

62 <h3>Explanation</h3>

63 <p>To find the square root, we need to find the sum of (9801 + 0). 9801 + 0 = 9801, and then √9801 = 99.</p>

64 <p>Therefore, the square root of (9801 + 0) is ±99.</p>

65 <p>Well explained 👍</p>

66 <h3>Problem 5</h3>

67 <p>Find the perimeter of the rectangle if its length ‘l’ is √9801 units and the width ‘w’ is 20 units.</p>

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

69 <p>We find the perimeter of the rectangle as 238 units.</p>

70 <h3>Explanation</h3>

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

72 <p>Perimeter = 2 × (√9801 + 20) = 2 × (99 + 20) = 2 × 119 = 238 units.</p>

73 <p>Well explained 👍</p>

74 <h2>FAQ on Square Root of 9801</h2>

75 <h3>1.What is √9801 in its simplest form?</h3>

76 <p>The prime factorization of 9801 is 3 × 3 × 3 × 3 × 11 × 11, so the simplest form of √9801 = 3 × 3 × 11 = 99.</p>

77 <h3>2.Mention the factors of 9801.</h3>

78 <p>Factors of 9801 are 1, 3, 9, 11, 33, 99, 121, 297, 363, 1089, 3267, and 9801.</p>

79 <h3>3.Calculate the square of 99.</h3>

80 <p>We get the square of 99 by multiplying the number by itself, that is 99 × 99 = 9801.</p>

81 <h3>4.Is 9801 a prime number?</h3>

82 <p>9801 is not a<a>prime number</a>, as it has more than two factors.</p>

83 <h3>5.9801 is divisible by?</h3>

84 <p>9801 has several factors; some of them are 1, 3, 9, 11, 33, 99, 121, 297, 363, 1089, 3267, and 9801.</p>

85 <h2>Important Glossaries for the Square Root of 9801</h2>

86 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 10^2 = 100, and the inverse of the square is the square root, that is, √100 = 10. </li>

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

88 <li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. Example: 81 is a perfect square because it is 9^2. </li>

89 <li><strong>Long division method:</strong>A mathematical method used to find the square root of a number through successive division. </li>

90 <li><strong>Prime factorization:</strong>The process of expressing a number as the product of its prime factors.</li>

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

92 <p>▶</p>

93 <h2>Jaskaran Singh Saluja</h2>

94 <h3>About the Author</h3>

95 <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>

96 <h3>Fun Fact</h3>

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