Simplifying radical expression $\sqrt[4]{3x}\cdot\sqrt{y+4}$

Question

I've never been any good with radicals... $$\sqrt[4]{3x}\cdot\sqrt{y+4}$$ Can anyone help with simplifying? Can I just square the inside of the first radical and then just multiply the two resulting square roots? Edit: Apparently this is the answer

$$\dfrac1{25x^4}$$

Answer 1

Iam not so sure about it

$\sqrt[4]{3x}\cdot\sqrt{y+4}$ be A

Then $A^4= 3x(y^2+16+8y) $

Simplifying $A^4$ we get

$3xy^2+ 48x+24xy=A^4$

Then A= $ \sqrt[4]{ 3xy^2+ 48x+24xy}$

Is it ok

Answer 2

You can write $\sqrt{\sqrt{3x}(y+4)}$ or $\sqrt[4]{3}\sqrt{\sqrt{x}(y+4)}$