Question

Докажите равенство.

​

Answer 1

$\sqrt{5 + 2 \sqrt{6} } = \sqrt{2} + \sqrt{3} \\ \sqrt{5 + 2 \times \sqrt{3} \times \sqrt{2} } = \sqrt{2} + \sqrt{3} \\ \sqrt{3 + 2 \sqrt{3 \times 2} + 2 } = \sqrt{2} = \sqrt{3} \\ \sqrt{ {( \sqrt{2} + \sqrt{3}) }^{2} } = \sqrt{2} + \sqrt{3} \\ \sqrt{2} + \sqrt{3} = \sqrt{2} + \sqrt{3}$