Answer:
(1) I and IV
Explanation:
For questions about rational numbers involving roots, it is helpful to know the numbers that are perfect squares. The first few* of them are ...
- 1 = 1²
- 4 = 2²
- 9 = 3²
- 16 = 4²
- 25 = 5²
So, if you see a number like 4 or 25 under the radical sign, you know that root is an integer, so is a rational number. Any other integer square roots (other than of perfect squares) will be irrational. That is √2 and √5 are irrational, because 2 and 5 are not perfect squares.
Of course, any integer, terminating decimal, repeating decimal, or fraction that is a ratio of integers is a rational number.
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Per the above, II and III are irrational numbers.
I has the value 0.
IV has the value 5.
Only I and IV are rational numbers.
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* We recommend learning the squares of numbers 1 to 20, and the cubes of numbers 1 to 10. These are the ones most commonly seen in algebra problems.