Square Root of 10.8
2026-02-28 10:14 Diff
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Last updated on August 5, 2025

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.

What is the Square Root of 10.8?

The square root is the inverse of the square of a number. 10.8 is not a perfect square. 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 exponential form. √10.8 ≈ 3.2863, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 10.8

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long division method and approximation method are used. Let us now learn the following methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 10.8 by Prime Factorization Method

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

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Square Root of 10.8 by Long Division Method

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

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

Step 2: Find the largest number whose square is less than or equal to the first pair (10). The largest number is 3 since 3 x 3 = 9.

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

Step 4: Double the quotient (3), which is 6, and use it as the next divisor's first digit.

Step 5: 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.

Step 6: Subtract 124 from 180 to get the remainder 56.

Step 7: Add a decimal point to the quotient and bring down two zeros, making the dividend 5600.

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

Step 9: The process continues similarly to obtain two decimal places for the square root value.

Thus, the square root of 10.8 is approximately 3.2863.

Square Root of 10.8 by Approximation Method

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:

Step 1: 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.

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

Thus, the approximate value of √10.8 is 3.2863.

Common Mistakes and How to Avoid Them in the Square Root of 10.8

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:

Problem 1

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

Okay, lets begin

The area of the square is 10.8 square units.

Explanation

The area of a square = side².

The side length is given as √10.8.

Area of the square = (√10.8)² = 10.8 square units.

Well explained 👍

Problem 2

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?

Okay, lets begin

5.4 square feet

Explanation

To find half of the building's area, divide the total area by 2.

Dividing 10.8 by 2 = 5.4

So half of the building measures 5.4 square feet.

Well explained 👍

Problem 3

Calculate √10.8 x 5.

Okay, lets begin

16.4315

Explanation

First, find the square root of 10.8, which is approximately 3.2863.

Then multiply 3.2863 by 5.

So, 3.2863 x 5 = 16.4315

Well explained 👍

Problem 4

What will be the square root of (10.8 + 5.2)?

Okay, lets begin

The square root is 4.

Explanation

To find the square root, first sum (10.8 + 5.2) = 16.

Then find the square root of 16, which is 4.

Therefore, the square root of (10.8 + 5.2) is ±4.

Well explained 👍

Problem 5

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

Okay, lets begin

The perimeter of the rectangle is 16.5726 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√10.8 + 5) ≈ 2 × (3.2863 + 5) = 16.5726 units.

Well explained 👍

FAQ on Square Root of 10.8

1.What is √10.8 in its simplest form?

Since 10.8 is not a perfect square, √10.8 is expressed in its simplest decimal form as approximately 3.2863.

2.Is 10.8 a perfect square?

No, 10.8 is not a perfect square because it does not have an integer as its square root.

3.Calculate the square of 10.8.

The square of 10.8 is calculated by multiplying the number by itself: 10.8 x 10.8 = 116.64

4.Is 10.8 a prime number?

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

5.What are the factors of 10.8?

Factors of 10.8, considering it as a decimal, include numbers like 1.08, 2.16, 5.4, and 10.8.

Important Glossaries for the Square Root of 10.8

  • Square root: 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.
     
  • Irrational number: An irrational number is a number that cannot be written as a fraction of two integers.
     
  • Decimal: A decimal consists of a whole number and a fraction represented together, such as 3.2863.
     
  • Long division method: A systematic approach to finding a square root by dividing the number into pairs of digits.
     
  • Approximation method: Estimating the square root of a number by comparing it to nearby perfect squares and using interpolation.

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Jaskaran Singh Saluja

About the Author

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.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.