Question

classify the numbers as rational or irrational.
π 4 π+4
rational irrational
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not feeling ready yeet? these can help:
simplify radical expressions
lesson: rational numbers
lesson: irrational numbers

Explanation:

Step1: Recall definitions

A rational number can be expressed as $\frac{a}{b}$ where $a,b$ are integers and $b
eq0$. An irrational number cannot be expressed as such, and $\pi$ is irrational.

Step2: Classify 4

4 can be written as $\frac{4}{1}$, so it is rational.

Step3: Classify $\pi$

$\pi$ is a non - repeating, non - terminating decimal, so it is irrational.

Step4: Classify $\pi + 4$

The sum of an irrational number ($\pi$) and a rational number (4) is irrational, because if $\pi+4$ were rational, then $\pi=(\pi + 4)-4$ would be rational (since the difference of two rationals is rational), which contradicts the fact that $\pi$ is irrational.

Answer:

rational: 4
irrational: $\pi$, $\pi + 4$