Determine which numbers in the set are irrational numbers. $1.222 \ldots , \frac { \sqrt { 5 } } { 2 } , 0 , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 9.090990999 \ldots , 5 \pi$
A) $\frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 5 \pi$
B) $\frac { \sqrt { 5 } } { 2 } , 0 , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 5 \pi$
C) $\frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , 9.090990999 \ldots , 5 \pi$
D) $1.222 \ldots , \frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 9.090990999 \ldots , 5 \pi$
E) $\frac { \sqrt { 5 } } { 2 } , - \frac { 14 \pi } { 3 } , 5 \pi$

Question

Quizplus · Accepted Answer

Irrational numbers cannot be expressed as a simple fraction. $\frac{\sqrt{5}}{2}$, $-\frac{14\pi}{3}$, $9.090990999\ldots$, and $5\pi$ are irrational. $\sqrt{64}$ is rational ($=8$), $1.222\ldots$ is rational ($=\frac{1222}{999}$), and $0$ is rational.

Determine Which Numbers in the Set Are Irrational Numbers 1.222…,52,0,−14π3,64,9.090990999…,5π1.222 \ldots , \frac { \sqrt { 5 } } { 2 } , 0 , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 9.090990999 \ldots , 5 \pi1.222…,25​​,0,−314π​,64​,9.090990999…,5π

Determine Which Numbers in the Set Are Irrational Numbers $1.222 \ldots , \frac { \sqrt { 5 } } { 2 } , 0 , - \frac { 14 \pi } { 3 } , \sqrt { 64 } , 9.090990999 \ldots , 5 \pi$