Question

What is `3/sqrt3`?

Answer 1

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

Explanation:

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)`.