How do you simplify sqrt27*sqrt33√27⋅√33?

2 Answers
Ella Labasbas
Feb 6, 2016

9sqrt√11

Explanation:

sqrt√27 * sqrt√33

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

Noah G
Feb 6, 2016

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

Explanation:

sqrt(27) = sqrt(9 xx 3)√27=√9×3

= 3sqrt(3)3√3

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

3sqrt(3) xx sqrt(33)3√3×√33

= 3sqrt(99)3√99

= 3sqrt(9 xx 11)3√9×11

= 3(3)sqrt(11)3(3)√11

= 9sqrt(11)9√11

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

Practice exercises:

  1. Simplify:

a) 3sqrt(5) xx 4sqrt(7)3√5×4√7

b) sqrt(24) xx 2sqrt(48)√24×2√48

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

Good Luck!

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