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[tex]\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
What kind of number is [tex]\bold{-\sqrt{2}}[/tex]?
[tex]\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]
First, let's look at each of the four sets of numbers:-
- Rational. This number set includes natural numbers (positive numbers only, like 1, 2, 3, 4, 5, 6...), zero, integers (negative & positive numbers and zero) and fractions (1/2, 1/3, 1/4...)
- Irrational. This set includes numbers that have an infinite quantity of digits after the decimal point. Also, irrational numbers cannot be written as fractions.
- Not a real number. This set includes imaginary numbers (yes, such numbers exist in mathematics, believe it or not)
- Natural number. As I said earlier, this set includes positive numbers only.
So in which set does [tex]\bold{-\sqrt{2}}[/tex] belong?
First, it's negative, so it's not a natural number.
Then, it's not an imaginary number, so it doesn't belong in the "Not a real number" set.
It can't be written as a fraction, so it doesn't belong in the "Rational" set, but it does belong in the "Irrational numbers" set.
According to the answer and explanation, we conclude that the number [tex]\bold{-\sqrt{2}}[/tex] belongs in the "Irrational number" set.
Good luck.
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