Question

√3(√6+√15) please simplify, thanks

Answer 1

Answer:
`3√(2)+3√(5)`

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Work Shown:

`√(3)\left(√(6)+√(15)\right)\\\\√(3)*√(6)+√(3)*√(15)\\\\√(3*6)+√(3*15)\\\\√(18)+√(3*3*5)\\\\√(9*2)+√(9*5)\\\\√(9)*√(2)+√(9)*√(5)\\\\3√(2)+3√(5)\\\\`

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Step-by-step explanation:

I distributed and used the idea that sqrt(A*B) = sqrt(A)*sqrt(B) to combine square roots, but also to break them up when factor out the largest perfect square factor.

Optionally for the last step, you could factor out 3, but your teacher may want you to leave it like shown.