Q. 202 - Intermediate Algebra

Question

In the following exercises, multiply:

$\left(\sqrt{11}+\sqrt{5}\right)\left(\sqrt{11}+6\sqrt{5}\right)$

Step-by-Step Solution

Answer

On multiplication we get, $41+7\sqrt{55}.$

Step 1. Multiply the given expression

The given expression is $\left(\sqrt{11}+\sqrt{5}\right)\left(\sqrt{11}+6\sqrt{5}\right)$

By multiplying we get,$11+6\sqrt{55}+\sqrt{55}+6·5$

Step 2. Simplify

By simplifying we get,

$$\begin{gathered} =11+6\sqrt{55}+\sqrt{55}+6·5 \\ =(11+30) + \sqrt{55}\left(6+1\right) \left[combine the like term\right] \\ =41+7\sqrt{55} \end{gathered}$$