Answer
$101+36\sqrt 5$
Work Step by Step
$(9+2\sqrt 5)^{2}$
=$(9+2\sqrt 5)(9+2\sqrt 5)$
=$9(9+2\sqrt 5)+2\sqrt 5(9+2\sqrt 5)$
=$81+18\sqrt 5+18\sqrt 5+2\sqrt 5(2\sqrt 5)$
=$81+(18+18)\sqrt 5+(2^{2})(\sqrt 5\times\sqrt 5)$
=$81+36\sqrt 5+4(5)$
=$81+36\sqrt 5+20$
=$81+20+36\sqrt 5$
=$101+36\sqrt 5$