Question

√(5-√(13+2√12)) упростить!!

Answer 1

$\sqrt{5-\sqrt{13+2\sqrt{12}}}=\sqrt{5-\sqrt{12+2\sqrt{12}+1}}=\sqrt{5-\sqrt{(\sqrt{12}+1)^{2}}}=\sqrt{5-(\sqrt{12}+1)}=\sqrt{5-\sqrt{12}-1}=\sqrt{4-2\sqrt{3}}=\sqrt{3-2\sqrt{3}+1}=\sqrt{(\sqrt{3}-1)^{2}}=|\sqrt{3}-1|=\sqrt{3}-1\\\\Otvet:\boxed{\sqrt{3}-1}$