Question

Which expression is equivalent to
`\sqrt128x^(8) y^(3) z^(9)`? 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

C on edge2020.

Explanation:

Trust me on this one.

:D

Answer 2

`(C)8x^4z^4√(2yz)`

Explanation:

We want to determine an expression equivalent to:
`√(128x^8y^3z^9)`

`√(ab) =√(a)*√(b)`

Therefore:

`√(128x^8y^3z^9)=√(128)*√(x^8)*√(y^3)*√(z^9)`

`=√(64*2)*\sqrt{x^(4*2)}*\sqrt{y^(2+1)}*\sqrt{z^(8+1)}\\=8√(2)*\sqrt{x^(4*2)}*√(y^2*y)*\sqrt{z^(8)*z}}`

`=8√(2)*x^4*y √(y)*z^4√(z)\\=8*x^4*z^4*√(2)*√(y)*√(z)\\=8x^4z^4√(2yz)`