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.

- Every irrational number is a real number.
- Every point on the number line is of the form \(\sqrt{m}\), where m is a natural number.
- Every real number is an irrational number.

Solution:

- True as a real number is either rational or irrational.
- False as numbers of other types also lie on the number line.
- 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 OP_{1} of unit length. Draw a liner segment P_{1}, P_{2} perpendicular to OP_{1} of unit length (see figure). Now draw a line segment P_{2}P_{3} perpendicular to OP_{2}. Then draw a line segment P_{3}P_{4} perpendicular to OP_{3}. Continuing in the manner, you can get the line segment P_{n-1}P_{n} by drawing a line segment of unit length perpendicular to OP_{n-1}. In this manner, you will have created the points P_{2}, P_{3}, … P_{n}, …. and joined them to create a beautiful spiral depicting \(\sqrt{2}\), \(\sqrt{3}\)\(\sqrt{4}\), ….

Solution:

Classroom activity – Do as directed.