Question
Which of the following is an irrational number? \( \sqrt{0} \) \( \sqrt{64} \)
Ask by Simmons Cross. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Neither √0 nor √64 is an irrational number.
Solution
We can determine whether a number is irrational by seeing if it can be expressed as a fraction of two integers.
1. √0 = 0, and 0 can be written as 0/1, so it is rational.
2. √64 = 8, and 8 can be written as 8/1, so it is also rational.
Therefore, neither √0 nor √64 is an irrational number.
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Simplify this solution Bonus Knowledge
Did you know that irrational numbers are those that cannot be expressed as a simple fraction, meaning their decimal representation goes on forever without repeating? Neither \( \sqrt{0} \) (which equals 0) nor \( \sqrt{64} \) (which equals 8) qualify as irrational numbers; both are whole numbers! If you’re curious about how to spot irrational numbers, look for roots of non-perfect squares (like \( \sqrt{2} \)) or the well-known \( \pi \) and \( e \). These quirky little numbers add a shape to the “number-verse” that’s anything but boring!
