Question

Rút gọn:

a) \(2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}\)

b) \(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\dfrac{8}{1-\sqrt{5}}\)

Answer 1

Lời giải:

a)

\(2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}\)

\(=2\sqrt{5}-\sqrt{25}.\sqrt{5}-\sqrt{16}.\sqrt{5}+\sqrt{121}.\sqrt{5}\)

\(=2\sqrt{5}-5\sqrt{5}-4\sqrt{5}+11\sqrt{5}=\sqrt{5}(2-5-4+11)=4\sqrt{5}\)

b)

\(\frac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\frac{8}{1-\sqrt{5}}=\frac{\sqrt{20}(\sqrt{5}+\sqrt{2})}{\sqrt{5}+\sqrt{2}}+\frac{8(1+\sqrt{5})}{(1-\sqrt{5})(1+\sqrt{5})}\)

\(=\sqrt{20}+\frac{8(1+\sqrt{5})}{1-5}=2\sqrt{5}-2(1+\sqrt{5})=-2\)