Question

rút gọn

\(a,\left(\sqrt{\dfrac{7-\sqrt{7}}{7}-2}\right)\left(\dfrac{6}{\sqrt{7}+1}+4\right)\)

\(b,\sqrt{\dfrac{5}{12}-\dfrac{1}{\sqrt{6}}}+\dfrac{1}{\sqrt{6}}\)

Answer 1

a:

Sửa đề: \(\left(\dfrac{7-\sqrt{7}}{\sqrt{7}}-2\right)\left(\dfrac{6}{\sqrt{7}+1}+4\right)\)

 \(=\left(\sqrt{7}-1-2\right)\left(\sqrt{7}-1+4\right)\)

\(=\left(\sqrt{7}-3\right)\left(\sqrt{7}+3\right)=7-9=-2\)

b: \(=\sqrt{\dfrac{5-2\sqrt{6}}{12}}+\dfrac{1}{\sqrt{6}}\)

\(=\dfrac{\sqrt{3}-\sqrt{2}}{2\sqrt{3}}+\dfrac{1}{\sqrt{6}}\)

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