RBSE Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2

Rajasthan Board RBSE Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2 Textbook Exercise Questions and Answers.

RBSE Class 9 Maths Solutions Chapter 1 Number Systems Exercise 1.2

Question 1.
State whether the following statements are true or false. Justify your answers.
(i) Every irrational number is a real number.
Answer:
True : Since collection of real numbers is made up of rational and irrational numbers.

(ii) Every point on the number line is of the form √m, where m is a natural number.
Answer:
False: Since numbers like \(\frac{5}{3}\), – 3, – \(\frac{5}{9}\), etc. are not of the form √m.

(iii) Every real number is an irrational number.
Answer:
False: 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.
Answer:
No, as √9 = 3 is a natural number as well as rational number.

Question 3.
Show how √5 can be represented on the number line.
Answer:
We draw a number line l and mark a point 0, representing zero (0), on it. Let point A represents 2 as shown in the figure. Now, construct a right-angled ∆OAB, right-angled at A such that OA = 2 units and AB = 1 unit (see figure).

By Pythagoras theorem, we have
OB = \(\sqrt{O A^{2}+A B^{2}}\) = \(\sqrt{4+1}\) = √5
Draw an arc with centre 0 and radius OB to cut the number line at C. Clearly, OC = OB = √5.
Then, the point C represents the irrational number √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 line segment P₁P₂ 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 OP₂. Continuing in this 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 P₂, P₃, ……. P_n, ……, and join them to create a beautiful spiral depicting √2 , √3 , √4, …….. .

Answer:
Do in your classroom, it is same as example 2.