How do you simplify #sqrt(400/5)#?

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Answer 1 · 2018-03-15T18:23:21

See below.

#sqrt(400/5) = sqrt(400)/sqrt(5)#

#sqrt(400)/sqrt(5)=20/sqrt5#

#=20/sqrt(5) * sqrt(5)/sqrt(5)#

#=(20sqrt(5))/5 = 4sqrt5#

Answer 2 · 2018-03-15T18:24:30

#sqrt(400/5)=4sqrt(5)#

#sqrt(400/5)=sqrt(400)/sqrt(5)=20/sqrt(5)#

We want to rationalize the denominator. Here we are just getting rid of the square root, shown in blue.

#20/sqrt(5)=(20color(blue)(sqrt(5)))/(sqrt(5)*color(blue)(sqrt(5)))=(20sqrt5)/5=4sqrt(5)#