How do you simplify #2sqrt7(3sqrt12 + 5sqrt8)#?

1 Answer
reudhreghs
Apr 4, 2016

#12sqrt21 + 20sqrt14#

Explanation:

Expand out the brackets first.

#2sqrt7(3sqrt12 + 5sqrt8) = 6sqrt12sqrt7 + 10sqrt7sqrt8#
# = 6sqrt84 + 10sqrt56#

Now simplify them as surds

#sqrt84 = sqrt4sqrt21 = 2sqrt21#
#sqrt56 = sqrt4sqrt14 = 2sqrt14#

#therefore 6sqrt84 + 10sqrt56 = 12sqrt21 + 20sqrt14#

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