How do you simplify 3/root3(6) ?

3 Answers
Sonnhard
Jul 11, 2018

root(3)(9/2)

Explanation:

we have
3/root(3)(6)=3/6^(1/3)*3*6^(-1/3)=3*3^(-1/3)*2^ (-1/3)=3^(2/3)/2^(1/3)=root(3)(9/2)

Harish Chandra Rajpoot
Jul 11, 2018

\root[3]{9/2}

Explanation:

Given that

3/\root[3]{6}

=\frac{\root[3]{3^3}}{\root[3]{6}}

=\root[3]{\frac{3^3}{6}}

=\root[3]{27/6}

=\root[3]{9/2}

George C.
Jul 11, 2018

3/root(3)(6) = root(3)(36)/2

Explanation:

To rationalise the denominator, we can proceed as follows:

3/root(3)(6) = (3 * root(3)(6^2))/(root(3)(6)root(3)(6^2))

color(white)(3/root(3)(6)) = (3root(3)(36))/(root(3)(6^3))

color(white)(3/root(3)(6)) = (3root(3)(36))/6

color(white)(3/root(3)(6)) = root(3)(36)/2

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