Question

18 multiple choice 2 points which is a rational number? √8 5√9 6√2 π 19 multiple choice 2 points which is an irrational number? √9 π -1/3 0 20 multiple choice 2 points which is an irrational number? √9 π -1/3 0

Explanation:

Step1: Recall rational - irrational number definitions

A rational number can be written as $\frac{p}{q}$ where $p,q$ are integers and $q
eq0$. Irrational numbers cannot be written in this form.

Step2: Analyze $\sqrt{8}$

$\sqrt{8}=2\sqrt{2}$, and $\sqrt{2}$ is irrational, so $\sqrt{8}$ is irrational.

Step3: Analyze $5\sqrt{9}$

$5\sqrt{9}=5\times3 = 15$, which can be written as $\frac{15}{1}$, so it is rational.

Step4: Analyze $6\sqrt{2}$

Since $\sqrt{2}$ is irrational, $6\sqrt{2}$ is irrational.

Step5: Analyze $\pi$

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

Step6: Analyze $\sqrt{9}$

$\sqrt{9}=3$, which is rational.

Step7: Analyze $-\frac{1}{3}$

It is in the form $\frac{p}{q}$ ($p=-1,q = 3$), so it is rational.

Step8: Analyze $0$

$0=\frac{0}{1}$, so it is rational.

Answer:

1. $5\sqrt{9}$
2. $\pi$
3. $\pi$