Answer:
the correct option is C i.e. [tex]8x^4yz^4\sqrt{2yz}[/tex]
Step-by-step explanation:
We need to solve the expression :
[tex]\sqrt{128x^8y^3z^9}[/tex]
Factors of 128 are: 2x2x2x2x2x2x2
and we know √ = 1/2
and √a.b = √a.√b
Solving:
[tex]=\sqrt{128x^8y^3z^9}\\\\=\sqrt{128} \sqrt{x^8} \sqrt{y^3} \sqrt{z^9}\\=\sqrt{2x2x2x2x2x2x2}\sqrt{x^8} \sqrt{y^2.y} \sqrt{z^8.z}\\=\sqrt{2^2x2^2x2^2x2}\sqrt{x^8} \sqrt{y^2.y} \sqrt{z^8.z}\\=(2^2)^{1/2} (2^2)^{1/2}(2^2)^{1/2} (2)^{1/2} (x^8)^{1/2} (y^2)^{1/2} (y)^{1/2} (z^8)^{1/2} z^{1/2}\\=2.2.2.(2)^{1/2}x^4y(y)^{1/2}z^4(z)^{1/2}\\=8x^4yz^4\sqrt{2yz}[/tex]
So, the correct option is C i.e. [tex]8x^4yz^4\sqrt{2yz}[/tex]
