# Bihar Board Class 9th Maths Solutions Chapter 1 Number Systems Ex 1.2

Bihar Board Class 9th Maths Solutions Chapter 1 Number Systems Ex 1.2 Textbook Questions and Answers.

## BSEB Bihar Board Class 9th Maths Solutions Chapter 1 Number Systems Ex 1.2

Question 1.
State whether the following statements are true or false. Justify your answers.

1. Every irrational number is a real number.
2. Every point on the number line is of the form $$\sqrt{m}$$, where m is a natural number.
3. Every real number is an irrational number.

Solution:

1. True as a real number is either rational or irrational.
2. False as numbers of other types also lie on the number line.
3. False as rational numbers are also real numbers.

Question 2.
Are the square roots of all positive integers irrational ? If not, give an example of the square root of a number that is a rational number.
Solution:
No, as $$\sqrt{4}$$ = 2 is a natural number

Question 3.
Show how $$\sqrt{5}$$ can be represented on the number line.
Solution:
We shall now show how to represent $$\sqrt{5}$$ on the number line.
We first represent $$\sqrt{5}$$ on the number line l. We construct s right-angled ∆ OAB, right-angled at A such that OA = 2 and AB = 1 unit (see figure).
Then, OB = $$\sqrt{\mathrm{OA}^{2}+\mathrm{AB}^{2}}$$ = $$\sqrt{4+1}$$ = $$\sqrt{5}$$
Now, we cut off a length OC = OB = $$\sqrt{5}$$ on the number line.
Then the point C represents the irrational number $$\sqrt{5}$$.

Question 4.
Classroom activity (Constructing the ‘square root spiral’) : Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion. Start with a point O and draw a line segment OP1 of unit length. Draw a liner segment P1, P2 perpendicular to OP1 of unit length (see figure). Now draw a line segment P2P3 perpendicular to OP2. Then draw a line segment P3P4 perpendicular to OP3. Continuing in the manner, you can get the line segment Pn-1Pn by drawing a line segment of unit length perpendicular to OPn-1. In this manner, you will have created the points P2, P3, … Pn, …. and joined them to create a beautiful spiral depicting $$\sqrt{2}$$, $$\sqrt{3}$$$$\sqrt{4}$$, ….
Solution:
Classroom activity – Do as directed.