Question

Find the value of √(8+2√15)+√(8-2√15)​

Answer 1

Step-by-step explanation:

$\sqrt{8 + 2 \sqrt{15} } + \sqrt{8 - 2 \sqrt{15} } \\ = \sqrt{5 + 3 + 2 \times \sqrt{5} \times \sqrt{3} } + \sqrt{5 + 3 - 2 \sqrt{5} \times \sqrt{3} } \\ = \sqrt{ { \sqrt{5} }^{2} + { \sqrt{3} }^{2} + 2 \sqrt{5 } \times \sqrt{3} } + \sqrt{ { \sqrt{5} }^{2} + { \sqrt{3} }^{2} - 2 \sqrt{5} \times \sqrt{3} } \\ = \sqrt{ {( \sqrt{5} + \sqrt{3} )}^{2} } + \sqrt{ {( \sqrt{5} - \sqrt{3} )}^{2} } = \\ = \sqrt{5} + \sqrt{3} + \sqrt{5} - \sqrt{3} \\ = 2 \sqrt{5}$