Simplifying The Square Root Of 108

Square Root of 108 How to Find the Square Root of 108? Cuemath from www.cuemath.com

Introduction

In mathematics, simplifying square roots is a common task that is often required in solving problems. When we simplify a square root, we try to express the number inside the radical sign in its simplest form. In this article, we will learn how to simplify the square root of 108.

What is a Square Root?

A square root is a number that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 multiplied by 3 is 9. The symbol for square root is √.

How to Simplify the Square Root of 108

To simplify the square root of 108, we need to find the factors of 108. We can start by dividing 108 by 2, which gives us 54. We can continue dividing by 2 until we get an odd number. 108 ÷ 2 = 54 54 ÷ 2 = 27 Now, we can see that 27 is a perfect cube. We can express 108 as the product of 27 and 4. 108 = 27 × 4 We can take the square root of 27 and simplify it to 3√3. We can leave 4 inside the radical sign because it is not a perfect square. √108 = √(27 × 4) = √27 × √4 = 3√3 × 2 = 2√27

What is the Simplified Form of the Square Root of 108?

The simplified form of the square root of 108 is 2√27. We can simplify this further by factoring out the perfect square factor of 27, which is 9. 2√27 = 2 × 3√3 = 6√3 Therefore, the simplified form of the square root of 108 is 6√3.

Why is it Important to Simplify Square Roots?

Simplifying square roots is important because it helps us to express numbers in their simplest form. It also allows us to manipulate expressions easily and perform operations such as addition, subtraction, multiplication, and division.

Examples of Simplifying Square Roots

Let's look at some examples of simplifying square roots. Example 1: Simplify √32 We can start by finding the factors of 32. 32 = 16 × 2 16 is a perfect square, so we can simplify the square root of 32 to 4√2. √32 = √(16 × 2) = √16 × √2 = 4√2 Example 2: Simplify √75 We can start by finding the factors of 75. 75 = 25 × 3 25 is a perfect square, so we can simplify the square root of 75 to 5√3. √75 = √(25 × 3) = √25 × √3 = 5√3

Conclusion

Simplifying the square root of 108 involves finding the factors of 108 and simplifying them to their simplest form. We can express the square root of 108 as 6√3, which is the simplified form. Simplifying square roots is important because it helps us to manipulate expressions easily and perform operations such as addition, subtraction, multiplication, and division.