1. ## Absolute Vaule

1. $\sqrt[4]{8x^5}$

$2|x|\sqrt{x}$

2. $\sqrt{49x^6}$

$7|x^3| or |7x^3$|? which one is valid?

3. $\sqrt{x^3}$

$|x|\sqrt{x}$?

2. ## Re: Absolute Vaule

How do you use absolute value for radicals?

3. ## Re: Absolute Vaule

Hi, are you working in $\mathbb{R}$? If so,
$|x|\sqrt{x}=x\sqrt{x}$ because the domain of $\sqrt{x}$ is $\mathbb{R}^+\cup{}\left\{0\right\}$

4. ## Re: Absolute Vaule

Originally Posted by theloser
[snip]
2. $\sqrt{49x^6}$

$7|x^3| or |7x^3$|? which one is valid?

[snip]
Both. But obviously the first is simpler.

And you should note that:

1. the domain of $\sqrt{x^n}$ is $x \geq 0$ if n is odd (why?) and so |x | = x under such circumstances.

2. the domain of $\sqrt{x^n}$ is $R$ if n is even (why?).