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Soros Olympiad in Mathematics
III Soros Olympiad 1996 - 97 (Russia)
9.1
rational? sum of third radicals (III Soros Olympiad 1996-97 R3 9.1)
rational? sum of third radicals (III Soros Olympiad 1996-97 R3 9.1)
Source:
May 31, 2024
algebra
Rational Root Theorem
Radicals
Problem Statement
Is rational or irrational,the number
(
2
25
3
+
15
3
+
9
3
+
1
9
3
+
6
3
+
4
3
)
×
(
25
3
+
10
3
+
4
3
)
?
\left(\dfrac{2}{\sqrt[3]{25}+\sqrt[3]{15}+\sqrt[3]{9}}+\dfrac{1}{\sqrt[3]{9}+\sqrt[3]{6}+\sqrt[3]{4}}\right) \times \left(\sqrt[3]{25}+\sqrt[3]{10}+\sqrt[3]{4}\right)?
(
3
25
+
3
15
+
3
9
2
+
3
9
+
3
6
+
3
4
1
)
×
(
3
25
+
3
10
+
3
4
)
?
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