Question

# Determine which statements are true and which are false. Prove those that are true and disprove those that are false.$\sqrt { 2 } / 6$is rational.

Solution

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DEFINITIONS

A real number $r$ is $\textbf{rational}$ if and only if there exists two integer $a$ and $b$ such that $r=\dfrac{a}{b}$ ($b\neq 0$).

$\textbf{Zero product property}$:

If the product of two real numbers is zero, then at least one of the real numbers is zero.

If the real numbers are both nonzero, then their product is also nonzero.

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