2019 Mock AMC 10B Problems/Problem 3

After trying each option we have \[\]A) $3^\frac{2018}{3}$ which is irrational as 2018 is not divisible by 3 \[\]B) $3^\frac{2019}{2}$ which is irrational as 2019 isn't divisible by 2 \[\]C) $3^2+\sqrt{2}^2+6\sqrt{2}$ which equals $11+6\sqrt{2}$ which is irrational \[\]D) $(2pi)^2$ equals $4pi^2$, which is irrational \[\]E) $(3-\sqrt{2})(3+\sqrt{2})=9-2=7$ which is rational We have $\boxed{\bold{E}}$ $(3-\sqrt{2})(3+\sqrt{2})$

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