Question

Simplify the following expression ${\left(\sqrt{5}+\sqrt{2}\right)}^2$

Answer 1

Given ${\left(\sqrt{5}+\sqrt{2}\right)}^2$

We know that ${\left(a+b\right)}^2=a^2+b^2+2ab$

Consider ${\left(\sqrt{5}+\sqrt{2}\right)}^2$

where $a=\sqrt{5},b=\sqrt{2}$

$$\begin{gathered} {\left(\sqrt{5}+\sqrt{2}\right)}^2={\left(\sqrt{5}\right)}^2+{\left(\sqrt{2}\right)}^2+2\sqrt{5}\sqrt{2} \\ =5+2+2\sqrt{10} \\ =7+2\sqrt{10} \end{gathered}$$

Hence, ${\left(\sqrt{5}+\sqrt{2}\right)}^2$ is $7+2\sqrt{10}$