How do you rationalize the denominator: #3/sqrt3#?

2 Answers
Mar 7, 2018

Answer:

#sqrt3#

Explanation:

This means that you do not want an irrational number (surd) in the denominator

#3/sqrt3 xx sqrt3/sqrt3" "larr sqrt3/sqrt3 =1#

#=(3sqrt3)/(sqrt3^2)#

#=(cancel3sqrt3)/cancel3#

#=sqrt3#

Mar 7, 2018

Answer:

#3/sqrt3=color(blue)((3sqrt3)/3#

Explanation:

Given:

#sqrt3#

Rationalize the denominator by multiplying the numerator and denominator by #sqrt3#.

#(3*sqrt3)/(sqrt3sqrt3)#

Apply the rule #sqrtasqrta=a#.

#(3sqrt3)/3#

Simplify.

#(color(red)cancel(color(black)(3))^1sqrt3)/color(red)cancel(color(black)(3))^1#

#sqrt3# #larr# answer