Question

How do you simplify `sqrt27*sqrt33`?

Answer 1

9`sqrt`11

Explanation:

`sqrt`27 * `sqrt`33

= [`sqrt`39] * [`sqrt`311]
= [3`sqrt`3] * [`sqrt`311] ; `sqrt`27 becomes 3`sqrt`3 because the sqrt of 9 is 3
= [3`sqrt`3] * [`sqrt`3] * [`sqrt`11] ; we separate `sqrt`3 and `sqrt`11
= 3`sqrt`3 `sqrt`11 ; we multiply those with `sqrt`3
= 3`sqrt`9 * `sqrt`11
= 3 * 3 * `sqrt`11 ; there are two 3s now because again the sqrt of 9 is 3
= 9`sqrt`11 ; FINAL ANSWER

Answer 2

First, before multiplying, you can simplify the √27.

Explanation:

`sqrt(27) = sqrt(9 xx 3)`

= `3sqrt(3)`

Now we can multiply, multiplying radicals with radicals and whole numbers with whole numbers.

`3sqrt(3) xx sqrt(33)`

= `3sqrt(99)`

= `3sqrt(9 xx 11)`

= `3(3)sqrt(11)`

= `9sqrt(11)`

So, `9sqrt(11)` is your answer, in simplest form.

Practice exercises:

1. Simplify:

a) `3sqrt(5) xx 4sqrt(7)`

b) `sqrt(24) xx 2sqrt(48)`

2 . Solve for x in `sqrt(6x) xx sqrt(2) = 2x`

Good Luck!