Prove that $(\sqrt{2} + \sqrt{5})$ is irrational.

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Step 1: Let us assume $\sqrt{2} + \sqrt{5}$ is rational number. Let $\sqrt{2} + \sqrt{5} = m$ where $m$ is rational
Step 2: $\Rightarrow (\sqrt{2} + \sqrt{5})^2 = m^2 \Rightarrow m^2 = 7 + 2\sqrt{10}$
Step 3: $\Rightarrow \sqrt{10} = \frac{m^2 - 7}{2}$. $\because m$ is rational $	herefore \frac{m^2 - 7}{2}$ is also rational
Step 4: But $\sqrt{10}$ is irrational $\Rightarrow$ LHS $
eq$ RHS. It means our assumption is wrong. Hence $\sqrt{2} + \sqrt{5}$ is an irrational number

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