Before doing any multiplication or division, we need to make sure the indices are the same. Multiplying radicals is simply multiplying the numbers inside the radical sign, the radicands, together. When dividing radicals, you can put both the numerator and denominator inside the same square roots.

#### Lessons

• Introduction
a)

• 1.
Write the following as a single radical = $\sqrt{x}$
a)
$\sqrt{3} \times \sqrt{8}$

b)
$\sqrt{7 \times 11}$

c)
$\sqrt{150} \over \sqrt{15}$

d)
$\frac{( \sqrt{20} \times \sqrt{5})} {\sqrt{64}}$

• 2.
a)
$\sqrt{45}$

b)
- $\sqrt{77}$

• 3.
-4$\sqrt{2}$ * - $\sqrt{2}$
5$\sqrt{2}$ * 6 $\sqrt{10}$ * 7 $\sqrt{50}$
$\sqrt{3 }$ ( $\sqrt{8} + 4)$
(4 $\sqrt{10 }$ - 3 $\sqrt{6}$ )(5 $\sqrt{2 } - \sqrt{5} )$