Q. 196 - Intermediate Algebra

Question

In the following exercises, multiply. $(8-\sqrt{2})(3+\sqrt{2})$

Step-by-Step Solution

Answer

On multiplication, we get $22+5\sqrt{2}$

Step 1: Given information

Given the expression $(8-\sqrt{2})(3+\sqrt{2})$$(8-\sqrt{2})(3+\sqrt{2})$

Step 2: Multiplying the terms and simplifying

Multiplying and simplifying we get

$$\begin{gathered} (8-\sqrt{2})(3+\sqrt{2})=24+8\sqrt{2}-3\sqrt{2}-\sqrt{(2{)}^2} \\ (8-\sqrt{2})(3+\sqrt{2})=24+8\sqrt{2}-3\sqrt{2}-2 \\ (8-\sqrt{2})(3+\sqrt{2})=(24-2)+8\sqrt{2}-3\sqrt{2} \\ (8-\sqrt{2})(3+\sqrt{2})=22+5\sqrt{2} \end{gathered}$$