Question

$(\sqrt{29*12\sqrt{5} } -\sqrt{29+12\sqrt{5} } )^{2}$

Answer 1

$(\sqrt{29-12\sqrt{5} } -\sqrt{29+12\sqrt{5} })^{2}=(\sqrt{9-12\sqrt{5} +20} - \sqrt{9+12\sqrt{5} +20})^{2}=(\sqrt{(3-2\sqrt{5})^{2} } -\sqrt{(3+2\sqrt{5} )^{2} })^{2}=(|3-2\sqrt{5}|-|3+2\sqrt{5}|)^{2}=(2\sqrt{5}-3-3-2\sqrt{5})^{2}=(-6)^{2}=36$