Asked by Alana
Determine if √8 is rational or irrational and give a reason for your answer.
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GPT 3.5
√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.
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.
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