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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 10.8.</p>

4 <h2>What is the Square Root of 10.8?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. 10.8 is not a<a>perfect square</a>. The square root of 10.8 is expressed in both radical and exponential forms. In the radical form, it is expressed as √10.8, whereas (10.8)^(1/2) is the<a>exponential form</a>. √10.8 ≈ 3.2863, 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 10.8</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the<a>long 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 10.8 by Prime Factorization Method</h2>

12 <p>The prime factorization method involves expressing a number as a<a>product</a>of prime<a>factors</a>. However, since 10.8 is not a perfect square and is a<a>decimal</a>, prime factorization is not suitable. We will use other methods like long<a>division</a>and approximation for non-integers.</p>

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15 <h2>Square Root of 10.8 by Long Division Method</h2>

14 <h2>Square Root of 10.8 by Long Division Method</h2>

16 <p>The long division method is particularly used for non-perfect square numbers. Below are the steps to find the<a>square root</a>of 10.8 using the long division method:</p>

15 <p>The long division method is particularly used for non-perfect square numbers. Below are the steps to find the<a>square root</a>of 10.8 using the long division method:</p>

17 <p><strong>Step 1:</strong>Pair the digits from right to left. For 10.8, treat it as 1080 for pairing by adding a zero.</p>

16 <p><strong>Step 1:</strong>Pair the digits from right to left. For 10.8, treat it as 1080 for pairing by adding a zero.</p>

18 <p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to the first pair (10). The largest number is 3 since 3 x 3 = 9.</p>

17 <p><strong>Step 2:</strong>Find the largest number whose square is<a>less than</a>or equal to the first pair (10). The largest number is 3 since 3 x 3 = 9.</p>

19 <p><strong>Step 3:</strong>Subtract 9 from 10, giving a<a>remainder</a>of 1, and bring down the next pair, making it 18.</p>

18 <p><strong>Step 3:</strong>Subtract 9 from 10, giving a<a>remainder</a>of 1, and bring down the next pair, making it 18.</p>

20 <p><strong>Step 4:</strong>Double the<a>quotient</a>(3), which is 6, and use it as the next<a>divisor</a>'s first digit.</p>

19 <p><strong>Step 4:</strong>Double the<a>quotient</a>(3), which is 6, and use it as the next<a>divisor</a>'s first digit.</p>

21 <p><strong>Step 5:</strong>Determine a digit (n) such that 6n x n is less than or equal to 180. Here n is 2 because 62 x 2 = 124.</p>

20 <p><strong>Step 5:</strong>Determine a digit (n) such that 6n x n is less than or equal to 180. Here n is 2 because 62 x 2 = 124.</p>

22 <p><strong>Step 6:</strong>Subtract 124 from 180 to get the remainder 56.</p>

21 <p><strong>Step 6:</strong>Subtract 124 from 180 to get the remainder 56.</p>

23 <p><strong>Step 7:</strong>Add a decimal point to the quotient and bring down two zeros, making the<a>dividend</a>5600.</p>

22 <p><strong>Step 7:</strong>Add a decimal point to the quotient and bring down two zeros, making the<a>dividend</a>5600.</p>

24 <p><strong>Step 8:</strong>Double the current quotient part (32), resulting in 64, and find a digit n such that 64n x n ≤ 5600.</p>

23 <p><strong>Step 8:</strong>Double the current quotient part (32), resulting in 64, and find a digit n such that 64n x n ≤ 5600.</p>

25 <p><strong>Step 9:</strong>The process continues similarly to obtain two decimal places for the square root value.</p>

24 <p><strong>Step 9:</strong>The process continues similarly to obtain two decimal places for the square root value.</p>

26 <p>Thus, the square root of 10.8 is approximately 3.2863.</p>

25 <p>Thus, the square root of 10.8 is approximately 3.2863.</p>

27 <h2>Square Root of 10.8 by Approximation Method</h2>

26 <h2>Square Root of 10.8 by Approximation Method</h2>

28 <p>The approximation method is another way to find the square roots. It's a simple method to estimate the square root of a given number. Here's how to find the square root of 10.8 using the approximation method:</p>

27 <p>The approximation method is another way to find the square roots. It's a simple method to estimate the square root of a given number. Here's how to find the square root of 10.8 using the approximation method:</p>

29 <p><strong>Step 1:</strong>Identify the closest perfect squares around 10.8. The smallest perfect square is 9, and the largest is 16. Therefore, √10.8 is between 3 and 4.</p>

28 <p><strong>Step 1:</strong>Identify the closest perfect squares around 10.8. The smallest perfect square is 9, and the largest is 16. Therefore, √10.8 is between 3 and 4.</p>

30 <p><strong>Step 2:</strong>Use linear interpolation to approximate: (10.8 - 9) / (16 - 9) = (x - 3) / (4 - 3) Solving gives x ≈ 3.2863.</p>

29 <p><strong>Step 2:</strong>Use linear interpolation to approximate: (10.8 - 9) / (16 - 9) = (x - 3) / (4 - 3) Solving gives x ≈ 3.2863.</p>

31 <p>Thus, the approximate value of √10.8 is 3.2863.</p>

30 <p>Thus, the approximate value of √10.8 is 3.2863.</p>

32 <h2>Common Mistakes and How to Avoid Them in the Square Root of 10.8</h2>

31 <h2>Common Mistakes and How to Avoid Them in the Square Root of 10.8</h2>

33 <p>Students often make mistakes when finding square roots, such as ignoring the negative square root or skipping steps in the long division method. Here are some mistakes to watch out for:</p>

32 <p>Students often make mistakes when finding square roots, such as ignoring the negative square root or skipping steps in the long division method. Here are some mistakes to watch out for:</p>

34 <h3>Problem 1</h3>

33 <h3>Problem 1</h3>

35 <p>Can you help Max find the area of a square box if its side length is given as √10.8?</p>

34 <p>Can you help Max find the area of a square box if its side length is given as √10.8?</p>

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

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

37 <p>The area of the square is 10.8 square units.</p>

36 <p>The area of the square is 10.8 square units.</p>

38 <h3>Explanation</h3>

37 <h3>Explanation</h3>

39 <p>The area of a square = side².</p>

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

40 <p>The side length is given as √10.8.</p>

39 <p>The side length is given as √10.8.</p>

41 <p>Area of the square = (√10.8)² = 10.8 square units.</p>

40 <p>Area of the square = (√10.8)² = 10.8 square units.</p>

42 <p>Well explained 👍</p>

41 <p>Well explained 👍</p>

43 <h3>Problem 2</h3>

42 <h3>Problem 2</h3>

44 <p>A square-shaped building measuring 10.8 square feet is built; if each of the sides is √10.8, what will be the square feet of half of the building?</p>

43 <p>A square-shaped building measuring 10.8 square feet is built; if each of the sides is √10.8, what will be the square feet of half of the building?</p>

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

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

46 <p>5.4 square feet</p>

45 <p>5.4 square feet</p>

47 <h3>Explanation</h3>

46 <h3>Explanation</h3>

48 <p>To find half of the building's area, divide the total area by 2.</p>

47 <p>To find half of the building's area, divide the total area by 2.</p>

49 <p>Dividing 10.8 by 2 = 5.4</p>

48 <p>Dividing 10.8 by 2 = 5.4</p>

50 <p>So half of the building measures 5.4 square feet.</p>

49 <p>So half of the building measures 5.4 square feet.</p>

51 <p>Well explained 👍</p>

50 <p>Well explained 👍</p>

52 <h3>Problem 3</h3>

51 <h3>Problem 3</h3>

53 <p>Calculate √10.8 x 5.</p>

52 <p>Calculate √10.8 x 5.</p>

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

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

55 <p>16.4315</p>

54 <p>16.4315</p>

56 <h3>Explanation</h3>

55 <h3>Explanation</h3>

57 <p>First, find the square root of 10.8, which is approximately 3.2863.</p>

56 <p>First, find the square root of 10.8, which is approximately 3.2863.</p>

58 <p>Then multiply 3.2863 by 5.</p>

57 <p>Then multiply 3.2863 by 5.</p>

59 <p>So, 3.2863 x 5 = 16.4315</p>

58 <p>So, 3.2863 x 5 = 16.4315</p>

60 <p>Well explained 👍</p>

59 <p>Well explained 👍</p>

61 <h3>Problem 4</h3>

60 <h3>Problem 4</h3>

62 <p>What will be the square root of (10.8 + 5.2)?</p>

61 <p>What will be the square root of (10.8 + 5.2)?</p>

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

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

64 <p>The square root is 4.</p>

63 <p>The square root is 4.</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

66 <p>To find the square root, first sum (10.8 + 5.2) = 16.</p>

65 <p>To find the square root, first sum (10.8 + 5.2) = 16.</p>

67 <p>Then find the square root of 16, which is 4.</p>

66 <p>Then find the square root of 16, which is 4.</p>

68 <p>Therefore, the square root of (10.8 + 5.2) is ±4.</p>

67 <p>Therefore, the square root of (10.8 + 5.2) is ±4.</p>

69 <p>Well explained 👍</p>

68 <p>Well explained 👍</p>

70 <h3>Problem 5</h3>

69 <h3>Problem 5</h3>

71 <p>Find the perimeter of a rectangle if its length 'l' is √10.8 units and the width 'w' is 5 units.</p>

70 <p>Find the perimeter of a rectangle if its length 'l' is √10.8 units and the width 'w' is 5 units.</p>

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

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

73 <p>The perimeter of the rectangle is 16.5726 units.</p>

72 <p>The perimeter of the rectangle is 16.5726 units.</p>

74 <h3>Explanation</h3>

73 <h3>Explanation</h3>

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

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

76 <p>Perimeter = 2 × (√10.8 + 5) ≈ 2 × (3.2863 + 5) = 16.5726 units.</p>

75 <p>Perimeter = 2 × (√10.8 + 5) ≈ 2 × (3.2863 + 5) = 16.5726 units.</p>

77 <p>Well explained 👍</p>

76 <p>Well explained 👍</p>

78 <h2>FAQ on Square Root of 10.8</h2>

77 <h2>FAQ on Square Root of 10.8</h2>

79 <h3>1.What is √10.8 in its simplest form?</h3>

78 <h3>1.What is √10.8 in its simplest form?</h3>

80 <p>Since 10.8 is not a perfect square, √10.8 is expressed in its simplest decimal form as approximately 3.2863.</p>

79 <p>Since 10.8 is not a perfect square, √10.8 is expressed in its simplest decimal form as approximately 3.2863.</p>

81 <h3>2.Is 10.8 a perfect square?</h3>

80 <h3>2.Is 10.8 a perfect square?</h3>

82 <p>No, 10.8 is not a perfect square because it does not have an integer as its square root.</p>

81 <p>No, 10.8 is not a perfect square because it does not have an integer as its square root.</p>

83 <h3>3.Calculate the square of 10.8.</h3>

82 <h3>3.Calculate the square of 10.8.</h3>

84 <p>The square of 10.8 is calculated by multiplying the number by itself: 10.8 x 10.8 = 116.64</p>

83 <p>The square of 10.8 is calculated by multiplying the number by itself: 10.8 x 10.8 = 116.64</p>

85 <h3>4.Is 10.8 a prime number?</h3>

84 <h3>4.Is 10.8 a prime number?</h3>

86 <p>No, 10.8 is not a<a>prime number</a>. It is a decimal and can be divided by numbers other than 1 and itself.</p>

85 <p>No, 10.8 is not a<a>prime number</a>. It is a decimal and can be divided by numbers other than 1 and itself.</p>

87 <h3>5.What are the factors of 10.8?</h3>

86 <h3>5.What are the factors of 10.8?</h3>

88 <p>Factors of 10.8, considering it as a decimal, include numbers like 1.08, 2.16, 5.4, and 10.8.</p>

87 <p>Factors of 10.8, considering it as a decimal, include numbers like 1.08, 2.16, 5.4, and 10.8.</p>

89 <h2>Important Glossaries for the Square Root of 10.8</h2>

88 <h2>Important Glossaries for the Square Root of 10.8</h2>

90 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, that is, √16 = 4. </li>

89 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, that is, √16 = 4. </li>

91 <li><strong>Irrational number:</strong>An irrational number is a number that cannot be written as a fraction of two integers. </li>

90 <li><strong>Irrational number:</strong>An irrational number is a number that cannot be written as a fraction of two integers. </li>

92 <li><strong>Decimal:</strong>A decimal consists of a whole number and a fraction represented together, such as 3.2863. </li>

91 <li><strong>Decimal:</strong>A decimal consists of a whole number and a fraction represented together, such as 3.2863. </li>

93 <li><strong>Long division method:</strong>A systematic approach to finding a square root by dividing the number into pairs of digits. </li>

92 <li><strong>Long division method:</strong>A systematic approach to finding a square root by dividing the number into pairs of digits. </li>

94 <li><strong>Approximation method:</strong>Estimating the square root of a number by comparing it to nearby perfect squares and using interpolation.</li>

93 <li><strong>Approximation method:</strong>Estimating the square root of a number by comparing it to nearby perfect squares and using interpolation.</li>

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

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

96 <p>▶</p>

95 <p>▶</p>

97 <h2>Jaskaran Singh Saluja</h2>

96 <h2>Jaskaran Singh Saluja</h2>

98 <h3>About the Author</h3>

97 <h3>About the Author</h3>

99 <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>

98 <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>

100 <h3>Fun Fact</h3>

99 <h3>Fun Fact</h3>

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

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