Question

Simplify square root 1/18

Answer 1

The square root of 1 is 1, but the square root of 18 needs to be explored.  18 is 9*2, and 9 is a perfect square.  So let's rewrite our original problem using that fact: $\sqrt{ \frac{1}{18} } = \sqrt{ \frac{1}{9*2} }$.  We can pull out the square root of 1 as 1 and the square root of 9 as 3, leaving the 2 behind: $\sqrt{ \frac{1}{9*2} } = \frac{1}{3} \sqrt{ \frac{1}{2} }$.  And there you go!

Answer 2

1/6 sqrt 2   Since 1/18 factors to 1/3 * 1/3 * 1/2  If you take the sqrt of 1/18 you will 1/3 sqrt 1/2 Since you cannot have a square root in the denominator, you must multiply denominator and numerator by sqrt 2 which will give you 1/3 sqrt 2/2 . Simplify to get sqrt 2/6