Question

What is equivalent to 9 3/4?

The answer is supposedly is 3 square root 3, but how is that the answer? can someone tell me the steps?

Answer 1

Explanation:

We need to say that
`9^(3/4)` is equivalent to what.

We know that, (3)² = 9

So,

`9^(3/4)=((3)^2)^(3/4)\\\\=3^(3/2)`

We can write
`3^(3/2) =3* 3^(1/2)`

And
`3^(1/2)=√(3)`

So,

`3* 3^(1/2)=3√(3)`

So,
`9^(3/4)` is equivalent to
`3√(3)`.

Hence, this is the required solution.