Square Root of 27 in Simplest Radical Form

The square root of 27 in simplest radical form is 3√3. In this post, we will learn how to find the simplified radical form of root 27.

How to Simplify Root 27

Question: Find the simplest radical form of square root of 27.

Answer:

To simplify the square root of 27 in simplest radical form, we need to follow the steps provided below.

Step 1: At first, we will factorize the number 27. Note that 27 is divisible by 3 and It can be written as

27 = 3 × 9 …(I)

And 9 can be expressed as

9 = 3 × 3 …(II)

Combining (I) and (II), we get that 27 = 3 × 3 × 3 …(∗)

This is the prime factorization of 27.

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

$\sqrt{27}$ $=\sqrt{3 \times 3 \times 3}$

= $\sqrt{3 \times 3}$ × √3

= 3 × √3 using the formula √(a×a) =a

= 3√3.

So 3√3 is the simplified radical form of the square root of 27. In other words,

√27 = 3√3

Therefore, √27 is an example of a quadratic surd.

Video Solution on How to Simplify Root 27:

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