How do you simplify #3/sqrt3#?

1 Answer
Feb 1, 2016

Since #3/sqrt(3)# has a radical in its denominator, you must do a process known as rationalization. Rationalization is when you must multiply the whole fraction by another fraction where the numerator and denominator are #sqrt(3)#. By doing so, you remove the radical, since #sqrt(3)# #(1.7320508...)# is irrational, that is, the decimal goes on forever without repeating.

#3/sqrt(3)color(red)(*sqrt(3)/sqrt(3))#

#=(3color(red)(*sqrt(3)))/(sqrt(3)color(red)(*sqrt(3)))#

#=(3sqrt(3))/3#

Notice how once you rationalize the fraction, the denominator is not irrational anymore. Also, keep in mind that you did not change the value of the simplified fraction. Since #sqrt(3)/sqrt(3)# is equal to #1#, you simply rearranged the way it was written. The value of the simplified fraction stays the same.