Let a be an integer. Prove that a^2 is divisible by 5 if and only if a is divisible by 5.
Now use that result to prove that there does not exist a rational number whose square is 5.
Let a be an integer. Prove that a^2 is divisible by 5 if and only if a is divisible by 5.
Now use that result to prove that there does not exist a rational number whose square is 5.