Question

Tính giá trị các biểu thức:

a/ \(\sqrt{7+\sqrt{7^2-4}}-\sqrt{7-\sqrt{7^2-4}}\)

b/ \(2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{48}}\)

c/ \(\left(\dfrac{1}{2+\sqrt{3}}-\dfrac{12}{3+\sqrt{3}}+\dfrac{26}{4-\sqrt{3}}\right)\cdot\left(4-3\sqrt{3}\right)\)

Answer 1

a: \(=\sqrt{7+\sqrt{45}}-\sqrt{7-\sqrt{45}}\)

\(=\dfrac{\sqrt{14+2\sqrt{45}}-\sqrt{14-2\sqrt{45}}}{\sqrt{2}}\)

\(=\dfrac{3+\sqrt{5}-3+\sqrt{5}}{\sqrt{2}}=\dfrac{2\sqrt{5}}{\sqrt{2}}=\sqrt{10}\)

b: \(=2\cdot\sqrt{80\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{20\sqrt{3}}\)

\(=\sqrt{\sqrt{3}}\left(2\cdot4\sqrt{5}-2\sqrt{5}-3\cdot2\sqrt{5}\right)\)

\(=\sqrt{\sqrt{3}}\cdot0=0\)

c: \(=\left(2-\sqrt{3}-6+2\sqrt{3}+8+2\sqrt{3}\right)\left(4-3\sqrt{3}\right)\)

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

=16-27=-11