How do you simplify 5 square root 10 times 2 square root 8?

1 Answer
Rafael
Sep 21, 2015

#40sqrt(5)#

Explanation:

Because these two radicals have the same index 2, you can easily multiply them.
#5sqrt10*2sqrt8#
#=(5)(2)sqrt(10*8)#
#=10sqrt(10*8)#
(We will factor 10 and 8)
#=10sqrt[(5*2)*(2*2*2)]#
#=10sqrt(5*2^4)#
(#2^4# is the square of #2^2#, so we can take that out of the square root symbol now)
#=10(2^2)sqrt(5)#
#=10(4)sqrt(5)#
#=40sqrt(5)#

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