What is #3/sqrt3#?

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Answer 1 · 2015-09-28T19:20:41

It's the same as #sqrt{3}#.

There are a few different ways this can be seen.

1) Rationalize the denominator:

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

2) Use properties of exponents:

#3/sqrt(3)=3^{1}/3^{1/2}=3^{1-1/2}=3^{1/2}=sqrt(3)#

3) Square it:

#(3/sqrt(3))^2=(3^2)/(sqrt(3)^2)=9/3=3#, hence #3/sqrt(3)=sqrt(3)#.