Question:- 1. state whether the following statements are true or false. Jutify your answer.

(a). Every irrational number is a real number.

(b.)Every point on the number line is of the form √m,where m is a natural number.

(c.) Every real number is an irrational number.

Solution:- 1.
(a)Consider the rational numbers and real numbers separately.

* The irrational numbers are that numbers which cannot be written in the form of p/q where p and q are integers and q≠ 0
(E.g.. √5, 6𝛑 , 0.022022022……)

* We already know that real number is a collection of rational numbers and irrational numbers .So,we got that ,every irrational number is a real number

(b)represent a number line. on number line ,we can represent negative as well as poitive numbers .

* positive numbers can be written in the form of √2,√2.2,√2.3,…….

* But we cannot write a negative number after taking square root of any number .

E.g. √-5=5i is a complex number (which you will be able to understand in higher class )

So,we got that every point on the number line is not in the form of √m where m is a natural number

(c) consider the irrational numbers and the real number separately .

* Irrational numbers are the numbers that cannot be written in the form of p/q where p and q are integers and q≠ 0.

* A real number is the collection of rational numbers and irrational numbers (e.g.√3, 3𝛑, 0.011011011)

So,we conclude that every irrational number is a real number.

Therefore .every real number is not an irrational number.

Quetion:- 2.Are the quare roots of all positive integers irrational ?If not , give an example of the square root of a number that is a rational number .

Solution:-As we know that sqiare root of every positive integer will not yield an integer (e.g.√3,√5,√7,…….)which are called irrational numbers.
But √9=3 which is an integer.
Therefore,we conclude that square root of every positive integer is not an irrational number.

Question:- 3.Show how √5 can be represented on the number line.

Solution:-Firt of all ,we have to draw a line segment AB of 2 unit on the number line.After then draw a prependicular line segment BC of 1 unit. After then join the points C and A to create a line segment AC.

Now, According to pythagorus theorem,