Question

Simplify.
Remove all perfect squares from inside the
square root.
V108​

Answer 1

Example: simplify √12

12 is 4 times 3:

√12 = √(4 × 3)
Use the rule:

√(4 × 3) = √4 × √3
And the square root of 4 is 2:

√4 × √3 = 2√3
So √12 is simpler as 2√3

Another example:

Example: simplify √8

√8 = √(4×2) = √4 × √2 = 2√2
(Because the square root of 4 is 2)

And another:

Example: simplify √18

√18 = √(9 × 2) = √9 × √2 = 3√2
It often helps to factor the numbers (into prime numbers is best):

Example: simplify √6 × √15

First we can combine the two numbers:

√6 × √15 = √(6 × 15)
Then we factor them:

√(6 × 15) = √(2 × 3 × 3 × 5)
Then we see two 3s, and decide to "pull them out":

√(2 × 3 × 3 × 5) = √(3 × 3) × √(2 × 5) = 3√10