Question

Please help with number 7

Answer 1

$\pi$ is a Irrational Number .

$\sqrt{12}$ is a Irrational Number .

3.14 is a Rational Number .

$4 . \overline{123}$ is a Rational Number .

$\sqrt{49}$  is Natural, Whole, Rational Number and Integer .

$-\frac{240}{6}$ 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 $\pi$ as a fraction of two integers and hence is Irrational.

$\sqrt{12}$ can be simplified as $\sqrt{(4 \times 3)}=2 \times \sqrt{3} \times \sqrt{3}$  again cannot represent the same as a fraction of two integers, and $\sqrt{12}$  is irrational.

3.14 can be represented in terms of $\frac{314}{100}=\frac{157}{50}$, and hence it is a Rational Number.

$4 . \overline{123}$ is the case of Repeating decimals, and repeating decimals are always Rational Numbers.

$\sqrt{49}$ is equal to 7 and hence is Natural Number. 7 can also be included in the whole number, rational number and Integer.

$-\frac{240}{6}$ is equal to -40, so it is Integer and Rational Number.