Question

plz solve this evaluate​

Answer 1

$\tt \sqrt{5+2\sqrt{6}} = ? \\ \\ \tt Let\: \sqrt{5+2\sqrt{6}} = \sqrt{a} + \sqrt{b} \\ \\ \tt Squaring\:on\:both\:sides \\ \\ \tt \implies {(\sqrt{5 + 2\sqrt{6}})}^{2} = { (\sqrt{a})}^{2} + {(\sqrt{b})}^{2} + 2\sqrt{a}.\sqrt{b} \\ \\ \tt \implies 5 + 2\sqrt{6} = a + b + 2 \sqrt{ab} \\ \\ \tt \implies a + b = 5 \\ \tt \implies 2\sqrt{ab} = 2\sqrt{6} \\ \\ \tt \implies ab = 6 \\ \\ \tt \implies a = 2 \: and \: b = 3 \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt \sqrt{5+2\sqrt{6}} = \sqrt{2}+\sqrt{3} }}}}$