Question

1. expressing \\(\sqrt{2}\\) as the ratio \\(\frac{\sqrt{2}}{1}\\) means the \\(\sqrt{2}\\) is a rational number.

Explanation:

Step1: Recall Rational Number Definition

A rational number is defined as a number that can be expressed as the ratio \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q
eq0\), and \(p\) and \(q\) have no common factors other than 1 (in simplest form).

Step2: Analyze \(\frac{\sqrt{2}}{1}\)

In the expression \(\frac{\sqrt{2}}{1}\), the numerator \(\sqrt{2}\) is an irrational number (it cannot be expressed as a fraction of two integers with no common factors other than 1). For a number to be rational, both \(p\) and \(q\) in \(\frac{p}{q}\) must be integers. Since \(\sqrt{2}\) is not an integer, \(\frac{\sqrt{2}}{1}\) does not satisfy the definition of a rational number. So, the statement is false.

Answer:

The statement is false.