Question

classify the numbers as rational or irrational. $sqrt{20}$, $-3$, $sqrt{20} + -3$
rational
irrational

Explanation:

Step1: Analyze $\sqrt{20}$

Simplify: $\sqrt{20} = \sqrt{4\times5} = 2\sqrt{5}$. Since $\sqrt{5}$ is non-terminating, non-repeating, $\sqrt{20}$ is irrational.

Step2: Analyze $-3$

Express as fraction: $-3 = \frac{-3}{1}$. It is a ratio of integers, so rational.

Step3: Analyze $\sqrt{20} + (-3)$

Sum of irrational and rational: $2\sqrt{5} - 3$. The result is non-terminating, non-repeating, so irrational.

Answer:

rational: $-3$
irrational: $\sqrt{20}$, $\sqrt{20} + (-3)$