Question

Вычислите.и если можно подробней.

Answer 1

$\sqrt{(\sqrt{3}-1)^2*2(2+\sqrt{3})} =\sqrt{(3-2\sqrt{3}+1)*2(2+\sqrt{3}) } =\\\sqrt{(4-2\sqrt{3})*2(2+\sqrt{3})} =\sqrt{(8-4\sqrt{3})(2+\sqrt{3}) } =\\\sqrt{16+8\sqrt{3} -8\sqrt{4}-12 }=\sqrt{4}=2\\\\\\ \sqrt{(\sqrt{5}+1)^2*2(3-\sqrt{5})} =\sqrt{(5+2\sqrt{5}+1)*2(3-\sqrt{5})}=\\ \sqrt{(6+2\sqrt{5})*2(3-\sqrt{5})}=\sqrt{(12+4\sqrt{5})(3-\sqrt{5})}=\\\sqrt{36-12\sqrt{5}+12\sqrt{5}-20}=\sqrt{16}=4$