Question

\(\sqrt{\left(2-\sqrt{5}\right)^2}-\dfrac{1}{2}\sqrt{20}\)

Answer 1

\(\sqrt{\left(2-\sqrt{5}\right)^2}-\dfrac{1}{2}\sqrt{20}\)

\(=\left|2-\sqrt{5}\right|-\dfrac{1}{2}\sqrt{2^2\cdot5}\)

\(=\sqrt{5}-2-\dfrac{1}{2}\cdot2\sqrt{5}\)

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

\(=-2\)

#\(Toru\)

Answer 2

\(\sqrt{\left(2-\sqrt{5}\right)^2}-\dfrac{1}{2}\sqrt{20}\)

\(=\left|2-\sqrt{5}\right|-\dfrac{1}{2}\cdot2\sqrt{5}\)

\(=-\left(2-\sqrt{5}\right)-\sqrt{5}\)

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

\(=-2\)