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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 various fields like physics, engineering, and finance. Here, we will discuss the square root of 9.8.</p>

4 <h2>What is the Square Root of 9.8?</h2>

5 <p>The<a>square</a>root is the inverse operation<a>of</a>squaring a<a>number</a>. 9.8 is not a<a>perfect square</a>. The square root of 9.8 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √9.8, whereas in the exponential form it is (9.8)^(1/2). √9.8 ≈ 3.1305, which is an<a>irrational number</a>because it cannot 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 9.8</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect squares like 9.8, approximation methods such as the long-<a>division</a>method are used. Let us now learn the following methods:</p>

8 <ul><li>Long division method</li>

9 <li>Approximation method</li>

10 </ul><h2>Square Root of 9.8 by Long Division Method</h2>

11 <p>The<a>long division</a>method is particularly used for non-perfect square numbers. Let us learn how to find the<a>square root</a>using the long division method, step by step:</p>

12 <p><strong>Step 1:</strong>Start by pairing the digits starting from the<a>decimal</a>point. For 9.8, treat it as 98 under the long division method.</p>

13 <p><strong>Step 2:</strong>Find a number whose square is<a>less than</a>or equal to 9. The closest is 3, since 3 x 3 = 9.</p>

14 <p><strong>Step 3:</strong>Subtract 9 from 9 to get 0, and bring down 80.</p>

15 <p><strong>Step 4:</strong>Double the<a>quotient</a>and bring it down as 6_, looking for a digit that fits.</p>

16 <p><strong>Step 5:</strong>Find a digit 'n' such that (60+n) x n ≤ 80. The suitable n is 1, as 61 x 1 = 61.</p>

17 <p><strong>Step 6:</strong>Subtract 61 from 80 to get 19, then bring down two zeros to get 1900.</p>

18 <p><strong>Step 7:</strong>Repeat the process, finding the next digit and quotient to approximate the square root further.</p>

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21 <h2>Square Root of 9.8 by Approximation Method</h2>

20 <h2>Square Root of 9.8 by Approximation Method</h2>

22 <p>Approximation method is another way to find square roots and is useful for quick estimates. Let's find the square root of 9.8 using this method:</p>

21 <p>Approximation method is another way to find square roots and is useful for quick estimates. Let's find the square root of 9.8 using this method:</p>

23 <p><strong>Step 1:</strong>Identify two perfect squares between which 9.8 falls. It lies between 9 (3^2) and 16 (4^2).</p>

22 <p><strong>Step 1:</strong>Identify two perfect squares between which 9.8 falls. It lies between 9 (3^2) and 16 (4^2).</p>

24 <p><strong>Step 2:</strong>Use linear approximation to find the decimal: (9.8 - 9) / (16 - 9) = 0.8 / 7 ≈ 0.1143</p>

23 <p><strong>Step 2:</strong>Use linear approximation to find the decimal: (9.8 - 9) / (16 - 9) = 0.8 / 7 ≈ 0.1143</p>

25 <p><strong>Step 3:</strong>Add this to the lower bound square root: 3 + 0.1143 ≈ 3.1143.</p>

24 <p><strong>Step 3:</strong>Add this to the lower bound square root: 3 + 0.1143 ≈ 3.1143.</p>

26 <p>Thus, the square root of 9.8 ≈ 3.1143.</p>

25 <p>Thus, the square root of 9.8 ≈ 3.1143.</p>

27 <h2>Common Mistakes and How to Avoid Them in Finding the Square Root of 9.8</h2>

26 <h2>Common Mistakes and How to Avoid Them in Finding the Square Root of 9.8</h2>

28 <p>Students make common mistakes when calculating square roots, like forgetting about negative roots or mishandling decimals. Here are some common pitfalls:</p>

27 <p>Students make common mistakes when calculating square roots, like forgetting about negative roots or mishandling decimals. Here are some common pitfalls:</p>

29 <h3>Problem 1</h3>

28 <h3>Problem 1</h3>

30 <p>Can you help Max find the area of a square box if its side length is given as √9.8?</p>

29 <p>Can you help Max find the area of a square box if its side length is given as √9.8?</p>

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

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

32 <p>The area of the square is approximately 9.8 square units.</p>

31 <p>The area of the square is approximately 9.8 square units.</p>

33 <h3>Explanation</h3>

32 <h3>Explanation</h3>

34 <p>The area of a square is given by side^2.</p>

33 <p>The area of a square is given by side^2.</p>

35 <p>The side length is √9.8.</p>

34 <p>The side length is √9.8.</p>

36 <p>Therefore, Area = (√9.8)^2 = 9.8.</p>

35 <p>Therefore, Area = (√9.8)^2 = 9.8.</p>

37 <p>Well explained 👍</p>

36 <p>Well explained 👍</p>

38 <h3>Problem 2</h3>

37 <h3>Problem 2</h3>

39 <p>A square-shaped garden measures 9.8 square meters. What is the length of one side?</p>

38 <p>A square-shaped garden measures 9.8 square meters. What is the length of one side?</p>

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

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

41 <p>The length of one side is approximately 3.1305 meters.</p>

40 <p>The length of one side is approximately 3.1305 meters.</p>

42 <h3>Explanation</h3>

41 <h3>Explanation</h3>

43 <p>The length of the side of the square is the square root of the area.</p>

42 <p>The length of the side of the square is the square root of the area.</p>

44 <p>Therefore, side = √9.8 ≈ 3.1305 meters.</p>

43 <p>Therefore, side = √9.8 ≈ 3.1305 meters.</p>

45 <p>Well explained 👍</p>

44 <p>Well explained 👍</p>

46 <h3>Problem 3</h3>

45 <h3>Problem 3</h3>

47 <p>Calculate √9.8 x 5.</p>

46 <p>Calculate √9.8 x 5.</p>

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

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

49 <p>Approximately 15.6525</p>

48 <p>Approximately 15.6525</p>

50 <h3>Explanation</h3>

49 <h3>Explanation</h3>

51 <p>First, find the square root of 9.8, which is approximately 3.1305.</p>

50 <p>First, find the square root of 9.8, which is approximately 3.1305.</p>

52 <p>Then multiply by 5: 3.1305 x 5 ≈ 15.6525.</p>

51 <p>Then multiply by 5: 3.1305 x 5 ≈ 15.6525.</p>

53 <p>Well explained 👍</p>

52 <p>Well explained 👍</p>

54 <h3>Problem 4</h3>

53 <h3>Problem 4</h3>

55 <p>What will be the square root of (9.8 + 6)?</p>

54 <p>What will be the square root of (9.8 + 6)?</p>

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

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

57 <p>The square root is approximately 4.</p>

56 <p>The square root is approximately 4.</p>

58 <h3>Explanation</h3>

57 <h3>Explanation</h3>

59 <p>First, calculate the sum: 9.8 + 6 = 15.8.</p>

58 <p>First, calculate the sum: 9.8 + 6 = 15.8.</p>

60 <p>Then, the square root of 15.8 is approximately 3.976.</p>

59 <p>Then, the square root of 15.8 is approximately 3.976.</p>

61 <p>Well explained 👍</p>

60 <p>Well explained 👍</p>

62 <h3>Problem 5</h3>

61 <h3>Problem 5</h3>

63 <p>Find the perimeter of a rectangle if its length ‘l’ is √9.8 units and the width ‘w’ is 5 units.</p>

62 <p>Find the perimeter of a rectangle if its length ‘l’ is √9.8 units and the width ‘w’ is 5 units.</p>

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

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

65 <p>The perimeter of the rectangle is approximately 16.261 units.</p>

64 <p>The perimeter of the rectangle is approximately 16.261 units.</p>

66 <h3>Explanation</h3>

65 <h3>Explanation</h3>

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

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

68 <p>Perimeter = 2 × (√9.8 + 5) = 2 × (3.1305 + 5) ≈ 2 × 8.1305 = 16.261 units.</p>

67 <p>Perimeter = 2 × (√9.8 + 5) = 2 × (3.1305 + 5) ≈ 2 × 8.1305 = 16.261 units.</p>

69 <p>Well explained 👍</p>

68 <p>Well explained 👍</p>

70 <h2>FAQ on Square Root of 9.8</h2>

69 <h2>FAQ on Square Root of 9.8</h2>

71 <h3>1.What is √9.8 in its simplest form?</h3>

70 <h3>1.What is √9.8 in its simplest form?</h3>

72 <p>The square root of 9.8 cannot be simplified further into a neat<a>fraction</a>or<a>whole number</a>. It is approximately 3.1305.</p>

71 <p>The square root of 9.8 cannot be simplified further into a neat<a>fraction</a>or<a>whole number</a>. It is approximately 3.1305.</p>

73 <h3>2.Can 9.8 be a perfect square?</h3>

72 <h3>2.Can 9.8 be a perfect square?</h3>

74 <p>No, 9.8 is not a perfect square because it does not result from squaring an integer.</p>

73 <p>No, 9.8 is not a perfect square because it does not result from squaring an integer.</p>

75 <h3>3.Calculate the square of 9.8.</h3>

74 <h3>3.Calculate the square of 9.8.</h3>

76 <p>The square of 9.8 is 9.8 × 9.8 = 96.04.</p>

75 <p>The square of 9.8 is 9.8 × 9.8 = 96.04.</p>

77 <h3>4.Is 9.8 a rational number?</h3>

76 <h3>4.Is 9.8 a rational number?</h3>

78 <p>Yes, 9.8 is a<a>rational number</a>because it can be expressed as a fraction: 98/10.</p>

77 <p>Yes, 9.8 is a<a>rational number</a>because it can be expressed as a fraction: 98/10.</p>

79 <h3>5.Is √9.8 a rational number?</h3>

78 <h3>5.Is √9.8 a rational number?</h3>

80 <p>No, √9.8 is an irrational number because it cannot be expressed as an exact fraction of two integers.</p>

79 <p>No, √9.8 is an irrational number because it cannot be expressed as an exact fraction of two integers.</p>

81 <h2>Important Glossaries for the Square Root of 9.8</h2>

80 <h2>Important Glossaries for the Square Root of 9.8</h2>

82 <ul><li><strong>Square root:</strong>The square root of a number is a value that, when multiplied by itself, gives the original number. Example: 3^2=9, so √9=3. </li>

81 <ul><li><strong>Square root:</strong>The square root of a number is a value that, when multiplied by itself, gives the original number. Example: 3^2=9, so √9=3. </li>

83 <li><strong>Irrational number:</strong>A number that cannot be expressed as a fraction of two integers. For example, √9.8 is irrational. </li>

82 <li><strong>Irrational number:</strong>A number that cannot be expressed as a fraction of two integers. For example, √9.8 is irrational. </li>

84 <li><strong>Approximation:</strong>The process of finding a value that is close enough to the right answer, usually within a specified range. </li>

83 <li><strong>Approximation:</strong>The process of finding a value that is close enough to the right answer, usually within a specified range. </li>

85 <li><strong>Perfect square:</strong>A number that is the square of an integer. For example, 9 is a perfect square since it is 3^2. </li>

84 <li><strong>Perfect square:</strong>A number that is the square of an integer. For example, 9 is a perfect square since it is 3^2. </li>

86 <li><strong>Long division method:</strong>A technique used to find the square root of numbers, especially non-perfect squares, using a step-by-step division process.</li>

85 <li><strong>Long division method:</strong>A technique used to find the square root of numbers, especially non-perfect squares, using a step-by-step division process.</li>

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

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

88 <p>▶</p>

87 <p>▶</p>

89 <h2>Jaskaran Singh Saluja</h2>

88 <h2>Jaskaran Singh Saluja</h2>

90 <h3>About the Author</h3>

89 <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>

90 <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>

91 <h3>Fun Fact</h3>

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

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