Question

this question has two parts. first, answer part a. then, answer part b. part a justify conclusions determine whether the statement is true or false. if the statement is true, explain your reasoning. if the statement is false, provide a counter - example or explain your reasoning. expressing $sqrt{2}$ as the ratio $\frac{sqrt{2}}{1}$ means that $sqrt{2}$ is a rational number. true false part b which of the following explains your reasoning or provides a counter example? a) rational numbers are numbers that are able to be put in the form $\frac{a}{b}$ (where $b
eq0$). b) rational numbers are numbers that are able to be put in the form $\frac{a}{b}$ (where $b
eq0$) and $a$ and $b$ are integers. $sqrt{2}$ is not an integer. c) rational numbers are numbers that are able to be put in the form $\frac{a}{b}$ (where $b
eq0$) and $a$ and $b$ are integers. $sqrt{2}$ is an integer. d) rational numbers are numbers that are able to be put in the form $\frac{a}{b}$ (where $b
eq0$) and $a$ and $b$ are rational numbers. $sqrt{2}$ is a rational number.

Explanation:

Step1: Recall definition of rational numbers

Rational numbers are of the form $\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b
eq0$.

Step2: Analyze $\sqrt{2}$

$\sqrt{2}$ is not an integer. A rational number must be expressible as a ratio of two integers. Just writing $\frac{\sqrt{2}}{1}$ does not make $\sqrt{2}$ rational since $\sqrt{2}$ is not an integer.

Answer:

Part A: False
Part B: B) Rational numbers are numbers that are able to be put in the form $\frac{a}{b}$ (where $b
eq0$) and $a$ and $b$ are integers. $\sqrt{2}$ is not an integer.