Respuesta :
Answer:
[tex]{22p^4qr\sqrt{35q[/tex]
Step-by-step explanation:
I am interpreting what you wrote as [tex]\sqrt{11p^4q^3r} \cdot2\sqrt{385p^4r}[/tex], sorry if that's not what you meant!
We rewrite [tex]385[/tex] as [tex]5 \cdot 7 \cdot 11[/tex]. Since the radicals have the same index, the expression can be written as
[tex]\sqrt{11p^4q^3r} \cdot2\sqrt{385p^4r}=2\sqrt{11p^4q^3r\cdot5\cdot7\cdot11p^4r}[/tex].
Multiplying like terms, the expression simplifies to
[tex]2\sqrt{5\cdot7\cdot11^2p^8q^3r^2}\\[/tex].
Taking out the perfect square factors, [tex]11^2, p^8, q^2,[/tex] and [tex]r^2,[/tex] we get
[tex]2\cdot11p^4qr\sqrt{5\cdot7q[/tex], or
[tex]\boxed{22p^4qr\sqrt{35q}}[/tex].
[tex]\begin{align*}\\\sqrt{11p^4q^3r} \cdot\sqrt{385p^4r}=\sqrt{11p^4q^3r\cdot5\cdot7\cdot11p^4r}\\=\sqrt{11^2p^8q^3r^2}\\\end{align*}[/tex][tex]\begin{align*}\sqrt{5*4}\\\end{align*}[/tex]
