# Math Help - Quotient and powers problem

1. ## Quotient and powers problem

Hello all,

I'm having one of those moments staring at some working in my textbook that I just can't get my head around. I'd rather have a poke in the right direction than a straight solution, but whatever is easier for you guys!

There are two steps in this working, I just cant see how to get from one to the next. I've tried writing it out in as many ways as I can think of, but I know I'm just missing that one tiny connection!

From this $\frac{1}{200}\frac{x^2+y^2}{\sqrt{x^2+y^2}}$ to this $\frac{1}{200}\sqrt{x^2+y^2}$

In fact, ignore the 1/200. It's just the second quotient I'm struggling with...

2. If we say that x^2 + y^2 = a

Then we have a/sqrt(a)

anything divided by the square root of itself = the square root of itself,

so a/sqrt(a) = sqrt(a) = sqrt(x^2 + y^2)

3. Originally Posted by sirellwood
If we say that x^2 + y^2 = a

Then we have a/sqrt(a)

anything divided by the square root of itself = the square root of itself,

so a/sqrt(a) = sqrt(a) = sqrt(x^2 + y^2)
And why does this work? Because, if a is positive,

$\frac{a}{\sqrt{a}}=\frac{\sqrt{a}\sqrt{a}}{\sqrt{a }}=\sqrt{a},$

by virtue of cancellation.

4. Multiply both numerator and denominator by $\sqrt{x^2 + y^2}$

5. Originally Posted by VincentP
Multiply both numerator and denominator by $\sqrt{x^2 + y^2}$
That works, too.