To determine if [tex]\(\sqrt{16}\)[/tex] is rational or irrational, we need to follow these steps:
1. Calculate [tex]\(\sqrt{16}\)[/tex]:
[tex]\[
\sqrt{16} = 4.0
\][/tex]
2. Define Rational and Irrational Numbers:
A rational number is any number that can be expressed as a fraction [tex]\(\frac{a}{b}\)[/tex], where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are integers and [tex]\(b \neq 0\)[/tex]. Rational numbers include all integers, finite decimals, and repeating decimals.
An irrational number is a number that cannot be expressed as a simple fraction; it has a non-repeating, non-terminating decimal expansion.
3. Check If the Result is Rational:
The result of [tex]\(\sqrt{16} = 4.0\)[/tex] is a finite decimal, which can be expressed as [tex]\(\frac{4}{1}\)[/tex]. Since [tex]\(4\)[/tex] and [tex]\(1\)[/tex] are integers, and [tex]\( \frac{4}{1}\)[/tex] is a simple fraction, this means that [tex]\( 4.0\)[/tex] is a rational number.
Therefore, [tex]\(\sqrt{16}\)[/tex] is rational because it simplifies to 4.0, which is a rational number.
