# Thread: Absolute Vaule

1. ## Absolute Vaule

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

$\displaystyle 2|x|\sqrt{x}$

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

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

3.$\displaystyle \sqrt{x^3}$

$\displaystyle |x|\sqrt{x}$?

2. ## Re: Absolute Vaule

How do you use absolute value for radicals?

3. ## Re: Absolute Vaule

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

4. ## Re: Absolute Vaule

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

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

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

And you should note that:

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

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