Question

\(\dfrac{5+2\sqrt{5}}{\sqrt{5}}+\sqrt{\left(3-\sqrt{5}\right)^2}\) rút gọn biểu thức

Answer 1

\(\dfrac{5+2\sqrt{5}}{\sqrt{5}}+\sqrt{\left(3-\sqrt{5}\right)^2}\\ =\dfrac{5+2\sqrt{5}}{\sqrt{5}}+3-\sqrt{5}\\ =\dfrac{5+2\sqrt{5}+\sqrt{5}.\left(3-\sqrt{5}\right)}{\sqrt{5}}\\ =\dfrac{5+2\sqrt{5}+3\sqrt{5}-5}{\sqrt{5}}\\ =\dfrac{5\sqrt{5}}{\sqrt{5}}=5\)

Answer 2

\(=\dfrac{\sqrt{5}\left(\sqrt{5}+2\right)}{\sqrt{5}}+\left|3-\sqrt{5}\right|\\ =\sqrt{5}+2+3-\sqrt{5}\\ =2+3=5\)

Answer 3

=\(\dfrac{\sqrt{5}\left(\sqrt{5}+2\right)}{\sqrt{5}}+\left|3-\sqrt{5}\right|\)

=\(\sqrt{5}+2+3-\sqrt{5}\)

=\(5\)