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27
Cubic Roots
Cubic Roots
Source:
January 1, 2006
geometry
3D geometry
Problem Statement
The sum
5
+
2
13
3
+
5
−
2
13
3
\sqrt[3] {5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}
3
5
+
2
13
+
3
5
−
2
13
equals
(A)
3
2
(B)
65
3
4
(C)
1
+
13
6
2
(D)
2
3
(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}
(A)
2
3
(B)
4
3
65
(C)
2
1
+
6
13
(D)
3
2
(E)
none of these
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