Thread: Multiplying Radicals

Stuck on a problem that I solved but doesnt look right to me for some reason.

Perform the indicated operation and simplify:

(2 √5 - 4 √6)(3 √3 + 8 √2)

So I used FOIL to expand.. not sure if people are familiar with the term (first term, outside/inside term, last term) and got.

(2 x 3)(√5 x √3) + (2 x 8)(√5 x √2) + (-4 x 3)(√6 x √3) + (-4 x 8)(√6 x √2)

Then simplified √18 and √12 further

6√15 + 16√10 - 12(3√2) - 32(2√3)

= 6√15 + 16√10 -36√2 - 64√3

.. Problem is I never learned a way to check your answer, if there is even one. Any clarification would greatly be appreciated.

It looks correct.

Thanks, Steve.

Originally Posted by danzig

Perform the indicated operation and simplify:

(2 √5 - 4 √6)(3 √3 + 8 √2)

So I used FOIL to expand.. not sure if people are familiar with the term (first term, outside/inside term, last term) and got.

(2 x 3)(√5 x √3) + (2 x 8)(√5 x √2) + (-4 x 3)(√6 x √3) + (-4 x 8)(√6 x √2)

Then simplified √18 and √12 further

6√15 + 16√10 - 12(3√2) - 32(2√3)

= 6√15 + 16√10 -36√2 - 64√3

.. Problem is I never learned a way to check your answer, if there is even one. Any clarification would greatly be appreciated.

Your answer is correct; to check, simply use calculator:

Initial expression: (2 √5 - 4 √6)(3 √3 + 8 √2) = -87.928597...

Your solution: 6√15 + 16√10 -36√2 - 64√3 = -87.928597...

NOTE: I meant your solution is correct mathematically;
I don't know the "format" your teacher expects.
Like: 2(3√15 + 8√10 -18√2 - 32√3) ?