Surds exam question rationalising

Question

This a surds question which is grade 8 according to the new GCSE'S which I have tried to work out but I keep getting the wrong answer.

Question: x is an integer such that:

${\frac{\sqrt {x} × \sqrt {18}}{\sqrt 3}}$ = ${8}{\sqrt 3}$

Find the value of x.

What I did:

${\frac{\sqrt {x} × \sqrt {18}}{\sqrt 3}}$ = ${8}{\sqrt 3}$ (×${\sqrt 3}$)

${\frac{\sqrt{54x}}{3}}$ = 24 (×3)

$\sqrt{54x}$ = 72 (×$\sqrt{}$)

54x = 5184 (÷54)

× = 96

Where did I go wrong?

Thank you and help is apprecaited

Answer 1

There is a mistake in the first step onthe left hand side as you multiply by $\sqrt{3}$.

The left hand side should be $\sqrt{18x}$.

It should be $$\sqrt{18x}=24$$

Answer 2

$$\frac{\sqrt{3}}{\sqrt{3}}=1\neq\frac{1}{3}$$

so the second step onwards is continued by

$$\sqrt{18x}=24$$ $$18x=24^2$$ $$x=\frac{24×24}{18}$$ $$x=32$$