Square Root of 18 in Simplest Radical Form

The square root of 18 in the simplest radical form is 3√2. In this post, we will learn how to find the simplified radical form of root 18.

How to Simplify Root 18

To simplify the square root of 18 in simplest radical form, we need to follow the steps provided below.

Step 1: At first, we will factorize the number 18. Note that 18 is an even number, so it will be divisible by 2. It can be written as

18 = 2 × 9 …(I)

And 9 can be expressed as

9 = 3 × 3 …(II)

Combining (I) and (II), we get that 18 = 2 × 3 × 3 …(∗)

This is the prime factorization of 18.

Step 2: Now, taking square root on both sides of (∗), we get that

$\sqrt{18}$ $=\sqrt{2 \times 3 \times 3}$

= $\sqrt{2}$ × $\sqrt{3 \times 3}$

= √2 × 3 using the formula √(a×a) =a

= 3√2.

So 3√2 is the simplified radical form of the square root of 18. In other words,

√18 = 3√2.

Video Solution on How to Simplify Root 18:

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