NCERT Solutions for Class 9 Mathematics Chapter-1 Number System Exercise 1.2Chapter-1 Number System Exercise 1.2

NCERT Solutions for Class 9 Mathematics Chapter-1 Number System 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.
(ii) Every point on the number line is of the form √m , where m is a natural number.
(iii) Every real number is an irrational number.
Solutions:
(i) True.
Because, Real number is the collection all the rational numbers and all irrational numbers .
(ii) False.
Reason: negative numbers cannot be the square root of any natural number.
(iii) False.
Because, rational numbers are also a part of the real numbers.

Class 9 Mathematics NCERT Ex 1.2

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, the square roots of all positive integers are not always irrational.

example:

if we take a positive integer, suppose 9, its square root is 3, which is a rational number.

Class 9 Mathematics NCERT Ex 1.2 Solutions

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

Solution:
First We Draw a number line and take point O and A on it such that lenght of OA = 1 unit.
Now,
Draw BA ⊥ OA as BA = 1 unit. Join OB = √2 units.
Now draw BB₁ ⊥ OB such that BB₁ =1 unit. Join OB₁ = √3 units.
Next, draw B₁B₂⊥ OB₁such that B₁B₂ = 1 unit.
Join OB₂ = units.
Again draw B₂B₃ ⊥OB₂ such that B₂B₃ = 1 unit.
Join OB₃ = √5 units.

Take O as centre and OB₃ as radius, draw an arc which cuts the number line at D.
This Point ‘D’ represents √5 on the number line.

Class 9 Mathematics NCERT Ex 1.2

Question-4.
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 lengths Draw a line 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 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 joined them to create a beautiful spiral depicting √2,√3,√4,……

Solution:
Try to do it by yourself.

NCERT Solutions for Class 9 Mathematics Chapter-1 Number System Exercise 1.2 ends.

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