What is (square root of [6] + 2 square root of [2])(4square root of [6] - 3 square root of 2)?

1 Answer
Sep 17, 2015

Answer:

#12 + 5sqrt12#

Explanation:

We multiply cross-multiply, that is,
#(sqrt6 + 2sqrt2)(4sqrt6 - 3sqrt2)#
equals
#sqrt6*4sqrt6 + 2sqrt2*4sqrt6 -sqrt6*3sqrt2 - 2sqrt2*3sqrt2#

The square roots time themselves equal the number under the root, so
#4*6 +8sqrt2sqrt6 - 3sqrt6sqrt2 - 6*2#

We put #sqrt2sqrt6# in evidence:
#24 + (8-3)sqrt6sqrt2 - 12#

We can join these two roots in one, after all #sqrtxsqrty = sqrt(xy)# as long as they're not both negative. So, we get
#24 + 5sqrt12 - 12#

Finally, we just take the difference of the two constants and call it a day
#12 + 5sqrt12#