Given the following expressions: which expression(s) result in a rational number?

  (1)  I and IV

Step-by-step 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 ...

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.

* 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.

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