Question

Which of the following is irrational?
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Answer 1

I can’t see the images you attached. Please either paste the four choices as text or upload the images again.

Meanwhile, here are quick rules to help you identify an irrational number so you can check the choices yourself:

- Any nonzero integer ratio a/b (with integers a, b and b ≠ 0) is rational. So if you can write the number as a fraction, it’s rational.
- A nonterminating, nonrepeating decimal is irrational; a terminating or repeating decimal is rational.
- sqrt(n) is irrational when n is a positive integer that is not a perfect square (e.g., sqrt(2), sqrt(3), sqrt(5) are irrational; sqrt(4)=2 is rational).
- nth root of an integer is irrational if the integer is not an nth power (e.g., cube root of 8 is 2 [rational], cube root of 2 is irrational).
- pi and e are irrational.
- Sums/products: rational + irrational or rational × irrational (with the rational ≠ 0) are irrational in most common cases, but check carefully (e.g., (1+√2) + (1−√2) = 2 rational).

If you paste the four options I’ll identify which one is irrational and show the reasoning.