How do you simplify 10 square root 6 times square root 2?

1 Answer
Aldrich
Sep 8, 2015

By using
#sqrt(a) xx sqrt(b) = sqrt(ab)#,

#10sqrt(6) xx sqrt(2) = 20sqrt(3)#

Explanation:

To simplify #10sqrt(6) xx sqrt(2)# we just need to keep in mind the following rule regarding radicals:

#sqrt(a) xx sqrt(b) = sqrt(ab)#

This means that:

#10sqrt(6) xx sqrt(2)#
#= 10sqrt(6*2#
#10sqrt(12)#

From this step, we need to check if we can factor out any perfect squares from #12#. If there is a perfect square, we can factor it out to simplify it more.

#4# is a perfect square, and we can factor out #4# from #12# since #12 = 4 xx 3#. We just apply the rule in reverse, splitting the radical.

#10sqrt(12)#
#=10sqrt(4 xx 3)#
#=10sqrt(4)xxsqrt(3)#
#=10xx2xxsqrt(3)#
#=20sqrt(3)#

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