Determine if √8 is rational or irrational and give a reason for your answer.

1 answer

√8 is irrational.

To determine if a number is rational or irrational, we need to consider its decimal representation. If the decimal representation is non-repeating and non-terminating, then the number is irrational.

√8 can be simplified as √(4 * 2) = √4 * √2 = 2 * √2.

Since √2 is irrational (proved by Pythagoras' theorem), 2 * √2 is also irrational.

Therefore, √8 is irrational.