Question

How do you simplify `3/root3(6)`?

Answer 1

`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)`

Answer 2

`\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}`

Answer 3

`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`