1. Simplify $\sqrt[3]{\frac{\sqrt{5}-1}{2}-\left(\frac{\sqrt{5}-1}{2}\right)^{2}}$ to get $\quad$.
(A) $\frac{\sqrt{5}-1}{2}$
(B) $\frac{\sqrt{5}+1}{2}$
(C) $\sqrt{5}$
(D) $\sqrt[3]{5}$
$-1 .(\mathrm{A})$
Let $\frac{\sqrt{5}-1}{2}=a$, then $a^{2}+a-1=0$, so $a^{3}+a^{2}-a=0$, which means $a^{3}=a-a^{2}$. Therefore, the original expression $=\sqrt[3]{a-a^{2}}=\sqrt[3]{a^{3}}=a$.