MathDB

9.1

Part of III Soros Olympiad 1996 - 97 (Russia)

Problems(3)

19...96 divisible by 1997 (III Soros Olympiad 1996-97 R1 9.1)

Source:

5/29/2024
In the middle of the number 1996 (i.e. between 1919 and 9696) you need to insert several digits so that the resulting number is divisible by 19971997. In this case, you need to get by with the least number of inserted digits.
number theory
|\sqrt[3]{5}-\sqrt3|-\sqrt3| ? 0.01 (III Soros Olympiad 1996-97 R2 9.1)

Source:

5/31/2024
Without using a calculator, find out which number is greater: ∣53−3∣−3∣    or    0.01|\sqrt[3]{5}-\sqrt3|-\sqrt3| \,\,\,\, \text{or} \,\,\,\, 0.01
algebraRadicals
rational? sum of third radicals (III Soros Olympiad 1996-97 R3 9.1)

Source:

5/31/2024
Is rational or irrational,the number (2253+153+93+193+63+43)×(253+103+43)?\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)?
algebraRational Root TheoremRadicals