Let $\alpha$ and $\beta$be the solutions of the quadratic equation${\mathrm{x}}^2-1154\mathrm{x}+1=0$, then ${\mathrm{\alpha }}^{\frac{1}{4}}+{\mathrm{\beta }}^{\frac{1}{4}}$is equal to

we have,
$\begin{array}{r}{x}^2-1154x+1=0\\ \alpha +\beta =1154,\alpha \beta =1\\ \Rightarrow (\sqrt{\alpha }+\sqrt{\beta }{)}^2=\alpha +\beta +2\sqrt{\alpha \beta }\\ =1154+2=1156\\ \Rightarrow \sqrt{\alpha }+\sqrt{\beta }=\sqrt{1156}=34\\ \text{ Again, }{\left({\alpha }^{1/4}+{\beta }^{1/4}\right)}^2=\sqrt{\alpha }+\sqrt{\beta }+2(\alpha \beta {)}^{1/4}\\ =34+2=36\\ \therefore \left({\alpha }^{1/4}+{\beta }^{1/4}\right)=\sqrt{36}=6\end{array}$