Question

Why in these types of questions(the image) I need to multiply the dominator by itself and by the nominator. and why I can't just multiply it just by itself.

Answer 1

`\frac{\sqrt{5x^(2) } }{\sqrt{3x^(3) } } =\sqrt{(5)/(3x) }`

Explanation:

Simply because

`A=(5)/(3) = (5)/(3)*(3)/(3) = (15)/(9) =(5)/(3)`

So its value remains Constant , It's simply as if you're multiplying by 1 which doesn't change anything at all

but when doing this

`A=(5)/(3) = (5)/(3)*(5)/(3) = (25)/(9) \\eq (5)/(3)\\`

You changed its value

`A` now became
`A^(2)`

Hope you understand it