Question

which choices if multiplied by $\frac{4}{9}$ would result in an irrational number answer? choose two.
a $pi$
b 3.4
c $sqrt{20}$
d $sqrt{64}$
e $\frac{15}{16}$

Explanation:

Step1: Recall rational/irrational rules

A non-zero rational number multiplied by an irrational number is irrational; rational × rational = rational. $\frac{4}{9}$ is rational.

Step2: Analyze Option A

$\pi$ is irrational. Calculate product: $\frac{4}{9} \times \pi = \frac{4\pi}{9}$, which is irrational.

Step3: Analyze Option B

$3.4 = \frac{17}{5}$, rational. Product: $\frac{4}{9} \times \frac{17}{5} = \frac{68}{45}$, rational.

Step4: Analyze Option C

$\sqrt{20} = 2\sqrt{5}$, irrational. Product: $\frac{4}{9} \times 2\sqrt{5} = \frac{8\sqrt{5}}{9}$, which is irrational.

Step5: Analyze Option D

$\sqrt{64} = 8$, rational. Product: $\frac{4}{9} \times 8 = \frac{32}{9}$, rational.

Step6: Analyze Option E

$\frac{12}{16} = \frac{3}{4}$, rational. Product: $\frac{4}{9} \times \frac{3}{4} = \frac{1}{3}$, rational.

Answer:

A. $\pi$, C. $\sqrt{20}$