How do you simplify #sqrt(5/7)*sqrt(2/5)#?

1 Answer
Rafael
Sep 29, 2015

#sqrt(14)/7#

Explanation:

Since the two radicals have the same index 2, you can combine them under one radical symbol.

#sqrt(5/7)*sqrt(2/5)#
#=sqrt(cancel5/7*2/cancel5)#
#=sqrt(2/7)#

You can leave it there, or you can continue by rationalizing it. To rationalize it, you have to take out the denominator out of the radical symbol.

#sqrt(2/7)#
#=sqrt(2/7*7/7)#
#=sqrt((2*7)/7^2)#
#=sqrt(2*7)/7#
#color(blue)(=sqrt(14)/7)#

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