Question

Solve the following:
${(\sqrt{{(\sqrt{5}-\frac{5}{2})}^2}-\sqrt[3]{3{(\frac{3}{2}-\sqrt{5})}^3})}^{1/2}-\sqrt{2}\sin \frac{7\pi }{4}$

Answer 1

$\left(\right(\sqrt{5}-\frac{5}{2}{)}^{2\times \frac{1}{2}}$-$(\frac{3}{2}-\sqrt{5}{)}^{3\times \frac{1}{3}}{)}^{\frac{1}{2}}$-$\sqrt{2}sin(2\pi -\frac{\pi }{4})$

$(\sqrt{5}-\frac{5}{2}-\frac{3}{2}+\sqrt{5}{)}^{\frac{1}{2}}-\sqrt{2}\times -\sqrt{2}$

$(2\sqrt{5}-4{)}^{\frac{1}{2}}+2$