Exponential Roots

Squareroots follow laws similar to laws of exponents, and are useful in rationalizing the denominator
$1. \;\; \sqrt{ab}=\sqrt a \times\sqrt b$
$2. \;\;\sqrt{\frac{a}{b}} = \frac{\sqrt a}{\sqrt b}$
$3. \;\; {(\sqrt a + \sqrt b)}^2 = a+2 \sqrt{ab}+b$
$4. \;\; (\sqrt a + \sqrt b) (\sqrt a - \sqrt b) = a-b$
$5. \;\;(a+\sqrt b) (a-\sqrt b) = a^2 -b$
$6. \;\; (\sqrt a + \sqrt b)(\sqrt c + \sqrt d) = \sqrt{ac} + \sqrt{ad} + \sqrt{bc} + \sqrt {bd}$