MathDB
Cubic Roots

Source:

January 1, 2006
geometry3D geometry

Problem Statement

The sum 5+2133+52133\sqrt[3] {5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}} equals (A) 32(B) 6534(C) 1+1362(D) 23(E) none of these\text{(A)} \ \frac 32 \qquad \text{(B)} \ \frac{\sqrt[3]{65}}{4} \qquad \text{(C)} \ \frac{1+\sqrt[6]{13}}{2} \qquad \text{(D)} \ \sqrt[3]{2} \qquad \text{(E)} \ \text{none of these}