Question

Which expression is equivalent to rmula1" title="\sqrt128x^{8} y^{3} z^{9}" alt="\sqrt128x^{8} y^{3} z^{9}" align="absmiddle" class="latex-formula">? Assume $y\geq 0$ and $z\geq 0$.
A - $2x^{2} z^{2} \sqrt8y^{3} z$

B - $4x^{2} yz^{3}\sqrt 2x^{2}$

C - $8x^{4} yz^{4} \sqrt2yz$

D - $64x^{4}yz^{4} \sqrt2yz$

Answer 1

Answer:

C on edge2020.

Step-by-step explanation:

Trust me on this one.

:D

Answer 2

Answer:

$(C)8x^4z^4\sqrt{2yz}$

Step-by-step explanation:

We want to determine an expression equivalent to: $\sqrt{128x^8y^3z^9}$

$\sqrt{ab} =\sqrt{a}*\sqrt{b}$

Therefore:

$\sqrt{128x^8y^3z^9}=\sqrt{128}*\sqrt{x^8}*\sqrt{y^3}*\sqrt{z^9}$

$=\sqrt{64*2}*\sqrt{x^{4*2}}*\sqrt{y^{2+1}}*\sqrt{z^{8+1}}\\=8\sqrt{2}*\sqrt{x^{4*2}}*\sqrt{y^2*y}*\sqrt{z^{8}*z}}$

$=8\sqrt{2}*x^4*y \sqrt{y}*z^4\sqrt{z}\\=8*x^4*z^4*\sqrt{2}*\sqrt{y}*\sqrt{z}\\=8x^4z^4\sqrt{2yz}$