algebra---------?

Question

can you factor xu out of sqrt[(x^2) + (x^2)(u^2)]

ifyou can then how??

Answer 1

Both answerers forgot to mention that sqrt x^2 = |x| (square root of x = absolute value of x). I will use V for sqrt

Check this: V(-2)^2 = V4 = 4

So, if you plug -2 in Vx^2 you get 2 that is actually -x. Pay lots of attention to this. Only if you know for sure tha x>=0 you can really do what they did. The rest of their replies is right, though. But only Doug showed you how to factor the u.

Think about this example, I guess that it will clarify this issue for you:

Let's say that you would have to find x in the equation

2x^2 + 4x - 5 = 0

x =( -4 +/- V56)/4

So, I want to simplify this.

x = (-4 +/- V8V7)/4

x= (-4 +/- 2V2V7)/4

I can simplify all this by 2 and I will get

x = (-2 +/- V14)/2

But, if I want to go on, I can do this

x = -2/2 +/- V14/2 = -1 +/- V(14/4) = -1 +/- V(7/2)


Ilusion

Answer 2

I can factor it out to: x (1 + u^2)^1/2

1. Factor out x^2
[(x^2) (1 + u^2)]^1/2

2. sqrt the x^2
[(x^2) (1 + u^2)]^1/2 = x (1 + u^2)^1/2

fyi: x^1/2 means sqrt of x

Answer 3

xu*√((1+u²)/u²)

Doug