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**rowdy3** Simplify the following radicals. Assume that the variables can represent a positive number.

square root of (4x)^2

Would that be 2x?

No because $\displaystyle \sqrt{(4x)^2}=\sqrt{16x^2}=4x$

cubed square root of -125d^3

Would that be 5d^3

No, because $\displaystyle \sqrt[3]{-125d^3}=-5d$

Find the domain of the given function.

f(x)=square root of 3x-8

I added 8. 3x is greater than 8/3.

My answer is (-infinity, 8/3]

No, because $\displaystyle 3x-8\geq0\Longrightarrow x\geq\frac{8}{3}$

$\displaystyle D=\left[\frac{8}{3},+\infty\right)$

Simplify

square root of 32x^5y^9

This is my answer. 2x^4y^3 square root 2xy^3

No, because $\displaystyle \sqrt{32 x^5 y^9}=\sqrt{16 \cdot 2 \cdot x^4 \cdot x \cdot y^8 \cdot y}=4x^2 y^4 \sqrt{2xy}$

Thanks.