which values are the result of cubing a rational number? check all that apply. 15 27 36 64 125 216

Explanation:

Step1: Recall the concept of cube - root of a number

A number $n$ is the cube of a rational number if $\sqrt[3]{n}$ is rational.

Step2: Calculate cube - roots of given numbers

For $n = 15$, $\sqrt[3]{15}\approx2.466$ (irrational). For $n = 27$, $\sqrt[3]{27}=3$ (rational since $3=\frac{3}{1}$). For $n = 36$, $\sqrt[3]{36}\approx3.302$ (irrational). For $n = 64$, $\sqrt[3]{64}=4$ (rational since $4 = \frac{4}{1}$). For $n = 125$, $\sqrt[3]{125}=5$ (rational since $5=\frac{5}{1}$). For $n = 216$, $\sqrt[3]{216}=6$ (rational since $6=\frac{6}{1}$).

Answer:

27, 64, 125, 216