Question

How do you simplify `3 /sqrt18`?

Answer 1

`sqrt2/2`

Explanation:

Turn `18` into a surd form, by looking at its factors and identifying square numbers and doing the following

`sqrt18 = sqrt(9* 2) = sqrt9 * sqrt2 = 3sqrt2`
`therefore sqrt18 = 3sqrt2`

Now substitute that into the fraction and simplify by cancelling out the `3`'s.

`3/sqrt18 = 3/(3sqrt2) = 1/sqrt2`

Rationalise the denominator, or make it not a square root by multiplying by `sqrt2/sqrt2`.

`1/sqrt2 * sqrt2/sqrt2 = sqrt2/2`