Question

Rút gọn

a) \(\left(\dfrac{\sqrt{5}-2}{\sqrt{5}+2}+1\right).\dfrac{1}{2}+\sqrt{\left(2-4\sqrt{5}\right)^2}\)

b) \(\left(4\sqrt{2}+\sqrt{30}\right).\left(\sqrt{5}-\sqrt{3}\right).\sqrt{4-\sqrt{15}}\)

Answer 1

\(\left(\dfrac{\sqrt{5}-2}{\sqrt{5}+2}+1\right)\cdot\dfrac{1}{2}+\sqrt{\left(2-4\sqrt{5}\right)^2}\\ =\left(\dfrac{\sqrt{5}-2}{\sqrt{5}+2}+\dfrac{\sqrt{5}+2}{\sqrt{5}+2}\right)\cdot\dfrac{1}{2}-\left(2-4\sqrt{5}\right)\\ =\left(\dfrac{\sqrt{5}-2+\sqrt{5}+2}{\sqrt{5}+2}\right)\cdot\dfrac{1}{2}-2+4\sqrt{5}\\ =\dfrac{1}{\sqrt{5}+2}\cdot\dfrac{1}{2}-2+4\sqrt{5}\\ =\dfrac{1}{2\sqrt{5}+4}-2+4\sqrt{5}\)Tớ chỉ giúp cậu tới đây thui. Còn lại bí rồi