Multiply (2 + √5)(3 + √5) and write the answer in the form a + b√5.

Rational plus irrational is irrational, while two irrational numbers can give either kind. $\sqrt{a}\,\sqrt{b} = \sqrt{ab}$, but $\sqrt{a} + \sqrt{b} \neq \sqrt{a + b}$. $(\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b}) = a - b$ and $(\sqrt{a} + \sqrt{b})^2 = a + b + 2\sqrt{ab}$.