## Precalculus: Mathematics for Calculus, 7th Edition

$|1-\sqrt{2}|=\sqrt{2}-1$
$|1-\sqrt{2}|$ Here, $\sqrt{2}\gt1$. This means that the substraction inside absolute value bars will result in a negative number. To express this quantity without the absolute value bars, we must change its sign. $|1-\sqrt{2}|=-(1-\sqrt{2})=\sqrt{2}-1$