How do you simplify (3√11+3√15)(3√3−2√2)?

1 Answer
AA_123
Apr 26, 2017

9√33−6√22+27√5−6√30

Explanation:

(3√11+3√15)(3√3−2√2)

Multiply each term in the bracket with each other term in the other bracket

3√11(3√3)+3√11(−2√2)+3√15(3√3)+3√15(−2√2)

Multiply the whole number with the whole number and the square root with the square root

3⋅3√11⋅3+3⋅−2√11⋅2+3⋅3√15⋅3+3⋅−2√15⋅2

9√33−6√22+9√45−6√30

9√45 can be simplified

9√45=9⋅√3⋅3⋅5=9⋅√32⋅5=9⋅√32⋅√5=9⋅3√5=27√5

So 9√33−6√22+9√45−6√30 can be rewritten as

9√33−6√22+27√5−6√30

These numbers can't be combined due to different numbers inside the roots, so this is the final answer.

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