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**TaylorM0192** Example: $\displaystyle (\sqrt{1-x^2})^2$

Inuitively, I would say it's simply $\displaystyle 1-x^2$. Alternatively $\displaystyle (\sqrt{1-x^2})(\sqrt{1-x^2})$ appears to give $\displaystyle \sqrt{1-2x^2+4x^2}$ which also does not seem correct.

The question arises from this problem:

$\displaystyle \sqrt{1+(\frac{x}{\sqrt{1-x^2}})^2}$ where I constantly get 1 by stating $\displaystyle \sqrt{1-x^2} = 1-x^2$. The correct answer, according to my text book anyway, is $\displaystyle \frac{1}{\sqrt{1-x^2}}$.

Thanks -