Question

which of the following shows that the quotient of two irrational numbers can be irrational? a. $5pi div pi$ b. $\frac{pi}{2} div pi$ c. $sqrt{2} div 2sqrt{5}$ d. $2sqrt{5} div sqrt{5}$

Explanation:

Step1: Evaluate Option A

$5\pi \div \pi = 5$, which is rational.

Step2: Evaluate Option B

$\frac{\pi}{2} \div \pi = \frac{1}{2}$, which is rational.

Step3: Evaluate Option C

$\sqrt{2} \div 2\sqrt{5} = \frac{\sqrt{2}}{2\sqrt{5}} = \frac{\sqrt{10}}{10}$. $\sqrt{10}$ is irrational, so $\frac{\sqrt{10}}{10}$ is irrational.

Step4: Evaluate Option D

$2\sqrt{5} \div \sqrt{5} = 2$, which is rational.

Answer:

C. $\sqrt{2} \div 2\sqrt{5}$