Q. 195 - Intermediate Algebra

Question

In the following exercises, multiply.

$(7+\sqrt{3})(9-\sqrt{3})$

Step-by-Step Solution

Answer

On multiplication, we get $60+2\sqrt{3}$

Step 1: Given information

Given the expression $(7+\sqrt{3})(9-\sqrt{3})$

Step 2: Multiplying the terms and simplifying

 Multiplying the terms and simplifying 

$$\begin{gathered} (7+\sqrt{3})(9-\sqrt{3})=7(9-\sqrt{3})+\sqrt{3}(9-\sqrt{3}) \\ (7+\sqrt{3})(9-\sqrt{3})=63-7\sqrt{3}+9\sqrt{3}-3 \\ (7+\sqrt{3})(9-\sqrt{3})=(63-3)-(7\sqrt{3}-9\sqrt{3}) \\ (7+\sqrt{3})(9-\sqrt{3})=60+2\sqrt{3} \end{gathered}$$