Maggie says, "The positive square root of a number is always less than the original number." Is this true?

Feb 9, 2016

No

Explanation:

Counter example:
$\textcolor{w h i t e}{\text{XXXXXX}} \sqrt{\frac{1}{4}} = \frac{1}{2}$

but $\frac{1}{2}$ is not less than the original number, $\frac{1}{4}$.

However, since I like Maggie, I will concede that her statement is true for all numbers greater than $1$