Question

Btt : 1 Rút gọn biểu thức :

a  \(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)

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

Answer 1

a/ \(\sqrt{9-4\sqrt{5}}-\sqrt{5}=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{5}=\sqrt{5}-2-\sqrt{5}=-2\)

b/ \(\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}=\frac{\sqrt{4-2\sqrt{3}}}{\sqrt{2}}+\frac{\sqrt{4+2\sqrt{3}}}{\sqrt{2}}\)

\(=\frac{\sqrt{\left(\sqrt{3}-1\right)^2}}{\sqrt{2}}+\frac{\sqrt{\left(\sqrt{3}+1\right)^2}}{\sqrt{2}}=\frac{\sqrt{3}-1+\sqrt{3}+1}{\sqrt{2}}=\frac{2\sqrt{3}}{\sqrt{2}}=\sqrt{6}\)

Answer 2

Chị @Hoàng Lê Bảo Ngọc giúp em.

Answer 3

a) \(\sqrt{9-4\sqrt{5}}-\sqrt{5}=\sqrt{\left(\sqrt{5}\right)^2-2\sqrt{5}\cdot2+2^2}-\sqrt{5}=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{5}=\sqrt{5}-2-\sqrt{5}=-2\)