14. Find the value of $(25+10 \sqrt{5})^{1 / 3}+(25-10 \sqrt{5})^{1 / 3}$.
14. Answer: 5
Let $x=(25+10 \sqrt{5})^{2 / 3}+(25-10 \sqrt{5})^{2 / 3}$. Then
$$
x^{3}=(25+10 \sqrt{5}+25-10 \sqrt{5})+3\left(25^{2}-100(5)\right)^{1 / 3}\left[(25+10 \sqrt{5})^{1 / 3}+(25-10 \sqrt{5})^{1 / 3}\right] \text {, }
$$
which gives $x^{3}=50+15 x$, or $(x-5)\left(x^{2}+5 x+10\right)=0$. This equation admits only one real root $x=5$.