9.4 Multiply square roots

Solution

ⓐ
$\begin{array}{cccc}& & & 3\left(5-\sqrt{2}\right)\hfill \\ \\ \\ \text{Distribute.}\hfill & & & 15-3\sqrt{2}\hfill \end{array}$

ⓑ
$\begin{array}{cccc}& & & \sqrt{2}\left(4-\sqrt{10}\right)\hfill \\ \\ \\ \text{Distribute.}\hfill & & & 4\sqrt{2}-\sqrt{20}\hfill \\ \\ \\ & & & 4\sqrt{2}-2\sqrt{5}\hfill \end{array}$

Solution

ⓐ
$\begin{array}{cccc}& & & \sqrt{5}\left(7+2\sqrt{5}\right)\hfill \\ \\ \\ \text{Multiply.}\hfill & & & 7\sqrt{5}+2·5\hfill \\ \\ \\ \text{Simplify.}\hfill & & & 7\sqrt{5}+10\hfill \\ \\ \\ & & & 10+7\sqrt{5}\hfill \end{array}$

ⓑ
$\begin{array}{cccc}& & & \sqrt{6}\left(\sqrt{2}+\sqrt{18}\right)\hfill \\ \\ \\ \text{Multiply.}\hfill & & & \sqrt{12}+\sqrt{108}\hfill \\ \\ \\ \text{Simplify.}\hfill & & & \sqrt{4}·\sqrt{3}+\sqrt{36}·\sqrt{3}\hfill \\ & & & 2\sqrt{3}+6\sqrt{3}\hfill \\ \\ \\ \text{Combine like radicals.}\hfill & & & 8\sqrt{3}\hfill \end{array}$

Solution

$\begin{array}{cccc}& & & \left(2+\sqrt{3}\right)\left(4-\sqrt{3}\right)\hfill \\ \text{Multiply.}\hfill & & & 8-2\sqrt{3}+4\sqrt{3}-3\hfill \\ \text{Combine like terms.}\hfill & & & 5+2\sqrt{3}\hfill \end{array}$

Solution

$\begin{array}{cccc}& & & \left(3-2\sqrt{7}\right)\left(4-2\sqrt{7}\right)\hfill \\ \\ \\ \text{Multiply.}\hfill & & & 12-6\sqrt{7}-8\sqrt{7}+4·7\hfill \\ \\ \\ \text{Simplify.}\hfill & & & 12-6\sqrt{7}-8\sqrt{7}+28\hfill \\ \\ \\ \text{Combine like terms.}\hfill & & & 40-14\sqrt{7}\hfill \end{array}$

Solution

$\begin{array}{cccc}& & & \left(3\sqrt{2}-\sqrt{5}\right)\left(\sqrt{2}+4\sqrt{5}\right)\hfill \\ \\ \\ \text{Multiply.}\hfill & & & 3·2+12\sqrt{10}-\sqrt{10}-4·5\hfill \\ \\ \\ \text{Simplify.}\hfill & & & 6+12\sqrt{10}-\sqrt{10}-20\hfill \\ \\ \\ \text{Combine like terms.}\hfill & & & \mathrm{-14}+11\sqrt{10}\hfill \end{array}$

Solution

$\begin{array}{cccc}& & & \left(4-2\sqrt{x}\right)\left(1+3\sqrt{x}\right)\hfill \\ \\ \\ \text{Multiply.}\hfill & & & 4+12\sqrt{x}-2\sqrt{x}-6x\hfill \\ \\ \\ \text{Combine like terms.}\hfill & & & 4+10\sqrt{x}-6x\hfill \end{array}$

Solution

Be sure to include the $2ab$ term when squaring a binomial.

1. ⓐ
   

   Multiply using the binomial square pattern.
   Simplify.
   Combine like terms.

2. ⓑ
   

   Multiply using the binomial square pattern.
   Simplify.
   Combine like terms.

Solution

Multiply using the binomial square pattern.
Simplify.

Solution

Multiply using the binomial square pattern.
Simplify.

Solution

Multiply using the binomial square pattern.
Simplify.