Question

In the following exercises, multiply.$(\sqrt{3}+\sqrt{10})(\sqrt{3}+2\sqrt{10})$

Short answer

On multiplication, we get $23+3\sqrt{30}$

Step-by-step solution

Given information

Given the expression$(\sqrt{3}+\sqrt{10})(\sqrt{3}+2\sqrt{10})$

Multiplying the terms and simplifying

Multiplying and simplifying, we get

$$\begin{gathered} (\sqrt{3}+\sqrt{10})(\sqrt{3}+2\sqrt{10})=\sqrt{(3{)}^2}+2\sqrt{30}+\sqrt{30}+2\sqrt{(10{)}^2} \\ (\sqrt{3}+\sqrt{10})(\sqrt{3}+2\sqrt{10})=3+2\sqrt{30}+\sqrt{30}+2·10 \\ (\sqrt{3}+\sqrt{10})(\sqrt{3}+2\sqrt{10})=(3+20)+(2\sqrt{30}+\sqrt{30}) \\ (\sqrt{3}+\sqrt{10})(\sqrt{3}+2\sqrt{10})=23+3\sqrt{30} \end{gathered}$$