Question

Prove that $5\surd 2$ is irrational.

Answer 1

Determine the proof of the expression $5\surd 2$ that is irrational.

Assume $5\surd 2$ is a rational number.

This is only conceivable if $5$ and $\sqrt{2}$ are both rational.

The product of two rational numbers is rational, as we know that $\sqrt{2}$ is irrational.

This contradicts our assumption that $5\surd 2$ is a rational number.

Hence, the number $5\surd 2$ is irrational.