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

1 Answer
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)