Q. 240 - Intermediate Algebra

Question

In the following exercises, multiply.

$(\sqrt{6}+\sqrt{3})(\sqrt{6}+6\sqrt{3})$

Step-by-Step Solution

Answer

The multiplication of $(\sqrt{6}+\sqrt{3})(\sqrt{6}+6\sqrt{3})$ is $24+21\sqrt{2}$

Step 1. Given

An expression $(\sqrt{6}+\sqrt{3})(\sqrt{6}+6\sqrt{3})$

To multiply the numbers.

Step 2. Multiply the expression

18+$(\sqrt{6}+\sqrt{3})(\sqrt{6}+6\sqrt{3})=\left(\sqrt{6^2}\right)+6\sqrt{6\times 3}+\sqrt{6\times 3}+6\left(\sqrt{3^2}\right)$

                                     $=6+6\sqrt{18}+\sqrt{18}+18$

                                     $=24+7\sqrt{18}$

Step 3. Simplify the expression

$(\sqrt{6}+\sqrt{3})(\sqrt{6}+6\sqrt{3})=24+7\sqrt{9\times 2}$

                                      $=24+7\sqrt{3^2}\sqrt{2}$

                                     $=24+7\left(3\sqrt{2}\right)$

                                     $=24+21\sqrt{2}$