What is 3/sqrt33√3?

1 Answer
Bill K.
Sep 28, 2015

It's the same as sqrt{3}√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)3√3=3√3⋅√3√3=3√33=√3

2) Use properties of exponents:

3/sqrt(3)=3^{1}/3^{1/2}=3^{1-1/2}=3^{1/2}=sqrt(3)3√3=31312=31−12=312=√3

3) Square it:

(3/sqrt(3))^2=(3^2)/(sqrt(3)^2)=9/3=3(3√3)2=32√32=93=3, hence 3/sqrt(3)=sqrt(3)3√3=√3.

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