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

Answer:

$\frac{\sqrt{5x^{2} } }{\sqrt{3x^{3} } } =\sqrt{\frac{5}{3x} }$

Step-by-step explanation:

Simply because

$A=\frac{5}{3} = \frac{5}{3}*\frac{3}{3} = \frac{15}{9} =\frac{5}{3}$

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

$A=\frac{5}{3} = \frac{5}{3}*\frac{5}{3} = \frac{25}{9} \neq \frac{5}{3}$

You changed its value

$A$ now became $A^{2}$

Hope you understand it