How do you simplify sqrt27*sqrt33?

2 Answers
Feb 6, 2016

9sqrt11

Explanation:

sqrt27 * sqrt33

= [sqrt39] * [sqrt311]
= [3sqrt3] * [sqrt311] ; sqrt27 becomes 3sqrt3 because the sqrt of 9 is 3
= [3sqrt3] * [sqrt3] * [sqrt11] ; we separate sqrt3 and sqrt11
= 3sqrt3
sqrt11 ; we multiply those with sqrt3
= 3sqrt9 * sqrt11
= 3 * 3 * sqrt11 ; there are two 3s now because again the sqrt of 9 is 3
= 9sqrt11 ; FINAL ANSWER

Feb 6, 2016

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!