Question

sums & products of rational & irrational numbers practice
complete this assessment to review what youve learned. it will not count toward your grade

what type of number will result from the sum of a rational number and irrational number?

1. irrational
2. rational
3. zero
4. equal

enter the number that corresponds to the correct answer.

(1 point)

option #□ describes the sum of a rational number and irrational number.

check answer remaining attempts : 3

Explanation:

By definition, a rational number can be written as $\frac{a}{b}$ where $a,b$ are integers ($b
eq0$), and an irrational number cannot be expressed this way. Using proof by contradiction: assume the sum of a rational $r$ and irrational $s$ is rational, so $r+s = t$ where $t$ is rational. Rearranging gives $s = t - r$. The difference of two rationals is rational, which contradicts $s$ being irrational. Thus the sum must be irrational.

Answer:

1. irrational