Question

Rút gọn: \(\sqrt{9-\sqrt{5\sqrt{3}+5\sqrt{8+10\sqrt{7-4\sqrt{3}}}}}\)

Answer 1

\(\sqrt{9-\sqrt{5\sqrt{3}+5\sqrt{8+10\sqrt{7-4\sqrt{3}}}}}\)

=\(\sqrt{9-\sqrt{5\sqrt{3}+5\sqrt{8+10\sqrt{4-2.2\sqrt{3}+3}}}}\)

=\(\sqrt{9-\sqrt{5\sqrt{3}+5\sqrt{8+10\sqrt{\left(2-\sqrt{3}\right)^2}}}}\)

=\(\sqrt{9-\sqrt{5\sqrt{3}+5\sqrt{8+10\left(2-\sqrt{3}\right)}}}\)

=\(\sqrt{9-\sqrt{5\sqrt{3}+5\sqrt{25-2.5\sqrt{3}+3}}}\)

=\(\sqrt{9-\sqrt{5\sqrt{3}+5\sqrt{\left(5-\sqrt{3}\right)^2}}}\)

=\(\sqrt{9-\sqrt{5\sqrt{3}+5\left(5-\sqrt{3}\right)}}\)

=\(\sqrt{9-\sqrt{25}}=\sqrt{9-5}=2\)

Answer 2

nếu có sai ở đâu thì nói mình biết nha