Question

Tính: \(A=(\sqrt{\sqrt{7+\sqrt{48}}}-\sqrt{\sqrt{28-16\sqrt{3}}})\sqrt{\sqrt{7+\sqrt{48}}}\)

GIÚP MK VS NHÉ :D

Answer 1

<=> A=\(\left(\sqrt{\sqrt{7+4\sqrt{3}}}-\sqrt{\sqrt{16-2.4.2\sqrt{3}+\left(2\sqrt{3}\right)^2}}\right)\sqrt{\sqrt{7+4\sqrt{3}}}\)

= \(\left(\sqrt{\sqrt{\left(2+\sqrt{3}\right)^2}}-\sqrt{\sqrt{\left(4-2\sqrt{3}\right)^2}}\right)\sqrt{\sqrt{\left(2+\sqrt{3}\right)^2}}\)

=\(\left(\sqrt{2+\sqrt{3}}-\sqrt{4-2\sqrt{3}}\right)\sqrt{2+\sqrt{3}}\)

= \(2+\sqrt{3}-\sqrt{\left(4-2\sqrt{3}\right)\left(2+\sqrt{3}\right)}\)

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

=\(2+\sqrt{3}-\sqrt{2\left(4-3\right)}\)

=\(2+\sqrt{3}-\sqrt{2}\)