9. Roots, Radicals, and Complex Numbers

Simplify the following.

$\sqrt{3}(2-\sqrt{6})$

Simplify the following.

$\sqrt{5x}(4+\sqrt{x})$

Rationalize the denominator.

$\frac{6+\sqrt{x}}{-\sqrt{x}}$

Rationalize the denominator and simplify the radical expression.

$\frac{2-\sqrt{3}}{2+\sqrt{3}}$

Rationalize the denominator. 

$-\frac{5}{2\sqrt{7}}$

Simplify the following.

$(4\sqrt{3}-5{)}^2$

Simplify the following.

$\left(2\sqrt{5}\right)\left(4\sqrt{7}\right)$

Rationalize the denominator and simplify the radical expression.

$\frac{\sqrt{7}}{5-\sqrt{6}}$

Simplify the following.

$\left(4\sqrt{x}\right)\left(3\sqrt{xy}\right)$