1. ## Intermediate Algebra

Simplify the following radicals. Assume that the variables can represent a positive number.
square root of (4x)^2
Would that be 2x?

cubed square root of -125d^3
Would that be 5d^3

Find the domain of the given function.
f(x)=square root of 3x-8
I added 8. 3x is greater than 8/3.

Simplify
square root of 32x^5y^9
This is my answer. 2x^4y^3 square root 2xy^3
Thanks.

2. Originally Posted by 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 $\sqrt{(4x)^2}=\sqrt{16x^2}=4x$

cubed square root of -125d^3
Would that be 5d^3

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

Find the domain of the given function.
f(x)=square root of 3x-8
I added 8. 3x is greater than 8/3.

No, because $3x-8\geq0\Longrightarrow x\geq\frac{8}{3}$
$D=\left[\frac{8}{3},+\infty\right)$

Simplify
square root of 32x^5y^9
This is my answer. 2x^4y^3 square root 2xy^3

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

Thanks.

Some solutions in Red.