Question

Assume a and b are non zero rational numbers and c is an irrational number. For each of the following expressions determine determine wether the result is irrational rational or both justify your answers?

Answer 1

Part A is irrational, but Parts B and C are both rational.

We know that Part A is irrational because an irrational number added to a rational number is still irrational. Also, an irrational number multiplied by a rational number is still irrational.

With Part B, we have an irrational number in the square root of 7. However, it is then squared to give us 7. This leaves us with 7 times a^2 which is rational. Two rational numbers multiplied still give us a rational number.

Finally, Part C only involves adding and multiplying rational numbers. Since that can only yield rational numbers, it must be rational.