Can someone help me simplify this please?

The question is 8/√2
Here's what I've got:
8/√2 = 8/√2 * √2/√2 = 8√2/√2
Is this correct?

no

you were correct at
8/√2 * √2/√2
= 8√2/(√2)^2 , but √2^2 is equal to 2
= 8√2/2
= 4√2

If you have any others, why not check your answer using a calculator
e.g. 8/√2 = 5.6568...
4√2 = 5.6568... my answer is correct