Question

Rút gọn:

a) \(\dfrac{\sqrt{7+4\sqrt{3}}}{\sqrt{3}+2}\)

b) \(\dfrac{\sqrt{9-4\sqrt{5}}}{2-\sqrt{5}}\)

Answer 1

a) ta có : \(\dfrac{\sqrt{7+4\sqrt{3}}}{\sqrt{3}+2}=\dfrac{\sqrt{\left(3+2.2\sqrt{3}+2^2\right)}}{\sqrt{3}+2}=\dfrac{\sqrt{\left(\sqrt{3}+2\right)^2}}{\sqrt{3}+2}\)

\(=\dfrac{\sqrt{3}+2}{\sqrt{3}+2}=1\)

b) ta có : \(\dfrac{\sqrt{9-4\sqrt{5}}}{2-\sqrt{5}}=\dfrac{\sqrt{\left(2^2-2.2\sqrt{5}+5\right)}}{2-\sqrt{5}}=\dfrac{\sqrt{\left(2-\sqrt{5}\right)^2}}{2-\sqrt{5}}\)

\(=\dfrac{2-\sqrt{5}}{2-\sqrt{5}}=1\)