To determine which number systems [tex]\(\frac{4}{\sqrt{36}}\)[/tex] belongs to, let's simplify the expression step-by-step.
1. Calculate [tex]\(\sqrt{36}\)[/tex]:
[tex]\[
\sqrt{36} = 6
\][/tex]
2. Simplify the fraction [tex]\(\frac{4}{\sqrt{36}}\)[/tex]:
[tex]\[
\frac{4}{\sqrt{36}} = \frac{4}{6} = \frac{2}{3}
\][/tex]
Now, [tex]\(\frac{2}{3}\)[/tex] is the simplified form of [tex]\(\frac{4}{\sqrt{36}}\)[/tex].
Next, we identify the number systems to which [tex]\(\frac{2}{3}\)[/tex] belongs:
- Rational Numbers (ℚ): Rational numbers are numbers that can be expressed as the quotient or fraction [tex]\(\frac{p}{q}\)[/tex], where [tex]\(p\)[/tex] and [tex]\(q\)[/tex] are integers and [tex]\(q \neq 0\)[/tex]. Since [tex]\(\frac{2}{3}\)[/tex] is a fraction with both the numerator (2) and the denominator (3) as integers, it is a rational number.
- Real Numbers (ℝ): Real numbers include all the rational numbers, irrational numbers (numbers that cannot be expressed as a simple fraction), and any number that can represent a point on a number line. Since [tex]\(\frac{2}{3}\)[/tex] is a rational number, it is also a real number.
Therefore, [tex]\(\frac{4}{\sqrt{36}}\)[/tex] belongs to the following number systems:
- Rational Numbers (ℚ)
- Real Numbers (ℝ)
