NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5.

• Number Systems Class 9 Ex 1.1
• Number Systems Class 9 Ex 1.2
• Number Systems Class 9 Ex 1.3
• Number Systems Class 9 Ex 1.4
• Number Systems Class 9 Ex 1.5
• Number Systems Class 9 Ex 1.6

Board	CBSE
Textbook	NCERT
Class	Class 9
Subject	Maths
Chapter	Chapter 1
Chapter Name	Number Systems
Exercise	Ex 1.5
Number of Questions Solved	5
Category	NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5

Ex 1.5 Class 9 Maths Question 1.
Classify the following numbers as rational or irrational:
(1) 2-
(2) (3+ )-
(3) 
(4) 
(5) 2π
Solution:
(1) Irrational ∵ 2 is a rational number and  is an irrational number.
∴ 2 –  is an irrational number.
(∵ The difference of a rational number and an irrational number is irrational)

(2) 3 +  –  = 3 (rational)

(3)  = (rational)

(4)  (irrational)  ∵ 1 ≠ 0 is a rational number and 2 ≠ 0 is an irrational a/2 number.
∴   = is an irrational number.
(∵ The quotient of a non-zero rational number with an irrational number is irrational).
(5) 2π (irrational) ∵ 2 is a rational number and π is an irrational number.
∴  2π is an irrational number, (∵ The product of a non-zero rational number with an irrational number is an irrational).

Ex 1.5 Class 9 Maths Question 2.
Simplify each of the following expressions :
(1) (3 +  ) (2 + a/2)
(2) (3 + ) (3- )
(3) ( +  )²
(4) ( –  ) ( +  )
Solution:

Ex 1.5 Class 9 Maths Question 3.
Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is
π = . This seems to contradict the fact that it is irrational. How will you resolve this contradiction?
Solution:
Actually  =  which is an approximate value of π.

Ex 1.5 Class 9 Maths Question 4.
Represent  on the number line.
Solution:
Mark the distance 9.3 units from a fixed point A on a given line to obtain a point B such that AB = 9.3 units. From B, mark a distance of 1 unit and mark the new point as C. Find the mid-point of AC and mark that point as O. Draw a semi-circle with center O and radius OC. Draw a line perpendicular to AC passing through B and intersecting the semi-circle at D

Then BD = . To represent  on the number line. Let us treat the line BC as the number line, with B as zero, C as 1, and so on. Draw an arc with center B and radius BD, which intersects the number line at point E. Then, the point E represent .

Ex 1.5 Class 9 Maths Question 5.
Rationalise the denominators of the following:
(i) 
(ii) 
(iii) 
(iv) 
Solution:

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