1. ## Square Root Simplification

(sqroot(x^3+x^2))/x

Anyone know how to simplify this?

2. Originally Posted by gearshifter
(sqroot(x^3+x^2))/x

Anyone know how to simplify this?
If this is what you wrote:

$\frac{\sqrt{x^3+x^2}}{x}$, then

$\frac{\sqrt{x^3+x^2}}{x}=\frac{\sqrt{x^2(x+1)}}{x} =\frac{x\sqrt{x+1}}{x}=\sqrt{x+1}$

3. how does $\frac{\sqrt{x^2(x+1)}}{x}$ equal $\frac{x \sqrt {x+1}}{x}$

?

4. Originally Posted by hana_102
how does $\frac{\sqrt{x^2(x+1)}}{x}$ equal $\frac{x \sqrt {x+1}}{x}$

?
Think of it like this

$[(x^2)(x+1)]^{\frac{1}{2}}$

Distribute the power of $\frac{1}{2}$

$x\sqrt{x+1}$

5. what if it was "For x0"?

6. Originally Posted by gearshifter
what if it was "For x0"?
If x=0 or x=-1, the radicand is 0.

If x<-1, the radicand is negative thus producing imaginary solutions.