[tex]\pi[/tex] is a Irrational Number
.
[tex]\sqrt{12}[/tex] is a Irrational Number
.
3.14 is a Rational Number
.
[tex]4 . \overline{123}[/tex] is a Rational Number
.
[tex]\sqrt{49}[/tex] is Natural, Whole, Rational Number and Integer
.
[tex]-\frac{240}{6}[/tex] is Integer and Rational number.
Explanation:
In order to answer this question, we need to know what are Natural Numbers, Whole Numbers, Integer, Rational and Irrational Numbers.
- Natural Numbers are those numbers which we use to count on a daily basis, starting from 1, 2, 3, and so on.
- Whole Numbers are simple the numbers including 0 along with Natural Numbers. Integers are Whole numbers including negative values as well with them.
- Any number which can be resembled as a fraction of two integers is known as Rational Number.
- Any number which is not Rational Number is known as Irrational Number, i.e., any number which cannot be represented as a fraction of two integers is known as Irrational Number.
We cannot represent [tex]\pi[/tex] as a fraction of two integers and hence is Irrational.
[tex]\sqrt{12}[/tex] can be simplified as [tex]\sqrt{(4 \times 3)}=2 \times \sqrt{3} \times \sqrt{3}[/tex] again cannot represent the same as a fraction of two integers, and [tex]\sqrt{12}[/tex] is irrational.
3.14 can be represented in terms of [tex]\frac{314}{100}=\frac{157}{50}[/tex], and hence it is a Rational Number.
[tex]4 . \overline{123}[/tex] is the case of Repeating decimals, and repeating decimals are always Rational Numbers.
[tex]\sqrt{49}[/tex] is equal to 7 and hence is Natural Number. 7 can also be included in the whole number, rational number and Integer.
[tex]-\frac{240}{6}[/tex] is equal to -40, so it is Integer and Rational Number.
