$\sqrt{a \pm b} \neq \sqrt{a} \pm \sqrt{b} $
$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b} $
$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} $
$\sqrt[n]{\sqrt[m]{a}} = \sqrt[n \times n]{a}$
$\sqrt[n]{a} = a^{\frac{1}{n}} \qquad \sqrt[n]{a^m} = a^{\frac{m}{n}}$
$\sqrt[-x]{a} = \frac{1}{\sqrt[x]{a}}$