Simplify Square Root of 8: Simplest Radical Form

The square root of 8 in the simplest radical form is 2√2. In this post, we will learn how to find the simplified radical form of root 8.

How to Simplify Root 8

To find the square root of 8 in simplest radical form, we need to follow the steps given below.

Step 1: At first, we will factorise the number 8. Note that 8 is an even number, so it will be divisible by 2 and we write

8 = 2 × 4.

Again 4 is an even number and 4 can be expressed as

4 = 2 × 2

Thus, 8 = 2 × 2 × 2 …(∗)

This 8 = 2 × 2 × 2 is the prime factorization of 8.

Step 2: Now, we will take square root on both sides of (∗). Thus we get that

√8 = $\sqrt{2 \times 2 \times 2}$

= √2 × $\sqrt{2 \times 2}$ using the rule of √(a×b) = √a ×√b.

= √2 × 2 using the formula √(a×a) =a

= 2√2.

So 2√2 is the simplified radical form of the square root of 8. In other words,

√8 = 2√2.

Video Solution on How to Simplify Root 8:

Also Read:

Square root of 50 simplified: The square root of 50 simplified is equal to 5√2, that is, √50=5√2.

FAQs