Simplifying a square root

1. Sep 3, 2009

Waggattack

1.I can't figure out how the $$\sqrt{1+((x^2)/(4-x^2))}$$ simplifies to 2 times$$\sqrt{1/(4-x^2)}$$

I have tried rewriting it in different ways, but I can't see how it simplifies. $$\sqrt{x^2 + 1/4-x^2}$$

2. Sep 3, 2009

w3390

The first thing to do is find a common denominator. Then you will be able to zero out some terms. Then, using the property of a square root, the square root of a fraction is the same as the square root of the numerator over the square root of the denominator. This will give you the answer.

3. Sep 3, 2009

PhaseShifter

It may help to rewrite these in a form where you don't need the parentheses.

$$\sqrt{1+{{x^2}\over{4-x^2}}}$$ simplifies to $$2\sqrt{{{1}\over{4-x^2}}}$$
Does that make it easier?

Last edited: Sep 3, 2009
4. Sep 4, 2009

njama

Hint: 1 in the square root, $$1=\frac{4-x^2}{4-x^2}$$

5. Sep 4, 2009

HallsofIvy

Staff Emeritus
In other words, write
$$1+\frac{x^2}{4-x^2}$$
as
$$\frac{4- x^2}{4- x^2}+ \frac{x^2}{4- x^2}$$