Question

How do you simplify `(9sqrt 2)/( 6sqrt 18)`?

Answer 1

Factor all the numbers as far as possible (`sqrt(2)` cannot be factored) and then cancel any terms which appear on top and bottom.

Explanation:

`(9sqrt(2))/(6sqrt(18)`

`=(3*3sqrt(2))/(3*2sqrt(3*3*2))`

`=(3*3sqrt(2))/(3*2*3sqrt(2))`

`=(cancel(3)*cancel(3)cancel(sqrt(2)))/(cancel(3)*2*cancel(3)*cancel(sqrt(2)))`

`=1/2`

Answer 2

`1/2`

Explanation:

first simplify `sqrt18 = sqrt(9 xx 2) =sqrt9 xxsqrt2 = 3sqrt2`

making use of : `sqrta xx sqrtb =sqrtab hArr sqrtab=sqrtaxxsqrtb`

`( 9sqrt2)/(6sqrt18) =( 9sqrt2)/(6xx3sqrt2)`

`=( 9cancel(sqrt2))/(18cancel(sqrt2)) = 9/18 = 1/2`