Question

1. circle all values that are rational numbers. 18 -√75 6 1/14 15/3 √6 ∛64 -√4

Explanation:

Step1: Recall rational number definition

A rational number can be written as a fraction $\frac{p}{q}$ where $p,q$ are integers and $q
eq0$, or as a terminating or repeating decimal.

Step2: Analyze 18

18 can be written as $\frac{18}{1}$, so it is rational.

Step3: Analyze $-\sqrt{75}$

$-\sqrt{75}=-5\sqrt{3}$, and $\sqrt{3}$ is irrational, so $-\sqrt{75}$ is irrational.

Step4: Analyze $6\frac{1}{14}$

$6\frac{1}{14}=\frac{6\times14 + 1}{14}=\frac{85}{14}$, so it is rational.

Step5: Analyze $\frac{15}{3}$

It is a fraction of integers, and $\frac{15}{3}=5$, so it is rational.

Step6: Analyze $\sqrt{6}$

$\sqrt{6}$ is an irrational number since it cannot be written as a fraction of two integers.

Step7: Analyze $\sqrt[3]{64}$

$\sqrt[3]{64}=4=\frac{4}{1}$, so it is rational.

Step8: Analyze $- 0.4$

$-0.4=-\frac{4}{10}=-\frac{2}{5}$, so it is rational.

Answer:

18, $6\frac{1}{14}$, $\frac{15}{3}$, $\sqrt[3]{64}$, $-0.4$