Question

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

Answer 1

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

We know that $\left(a+b\right)\left(a-b\right)=a^2-b^2$

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

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

$$\begin{gathered} {\left(\sqrt{5}\right)}^2-{\left(\sqrt{2}\right)}^2 \\ 5-2 \\ 3 \end{gathered}$$

Hence, $\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)$ is $3$