Question

which is the most specific subset in which the number below belongs to?*\\( \sqrt { 36 } \\)wholeintegernaturalrationalirrational

Explanation:

Step1: Calculate the value of \(\sqrt{36}\)

\(\sqrt{36} = 6\)

Step2: Analyze the properties of the number 6

• Natural numbers: Natural numbers are positive integers starting from 1 (\(1,2,3,\cdots\)). Since \(6>0\) and is an integer, \(6\) is a natural number.
• Whole numbers: Whole numbers are non - negative integers (\(0,1,2,\cdots\)). While \(6\) is a whole number, the set of natural numbers is a more specific subset than whole numbers (as natural numbers do not include \(0\)).
• Integers: Integers include positive and negative whole numbers and \(0\) (\(\cdots,- 2,-1,0,1,2,\cdots\)). But natural numbers (a subset of integers) are more specific.
• Rational numbers: Rational numbers are numbers that can be written as \(\frac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b

eq0\). Since \(6=\frac{6}{1}\), it is rational. But natural numbers (a subset of rational numbers) are more specific.

• Irrational numbers: Irrational numbers cannot be written as a fraction \(\frac{a}{b}\). Since \(6\) is rational, it is not irrational.

Answer:

natural