# Important Questions for Class 9 Chapter 1- Numbers System

If you are preparing for your final exam or any other test, you can use this free set of important questions for CBSE class 9th maths PDF for practice.

Important questions based on NCERT syllabus for Class 9 Chapter 1-Rational Numbers:

Question 1: Expand (2+√2)^2. Is it rational?
Solution:
(2+√2)^2 = 2^2+ 2 x 2 + √2 + √(2^2)
= 4 + 2 + 4√2
= 6 + 4√2
The obtained value contiains a rational and an irrational part. Hence it is not rational.

Question 2: Find 4 rational numbers between 3/5 and 4/5 using d=(y−x)/n+1
Solution:
x = 3/5 and y = 4/5
We have to find 4 rational numbers
i.e, n = 4
Using d = (y−x)/n+1
= (4/5−3/5)/5
= 1/25
Hence 4 rational numbers are 16/25, 17/25, 18/25 and 19/25

Question 3: Rationalize the denominator of the following:
1/ (√7 - √6.
Solution:
1/(√7- √6) = (1(√7+ √6))/(√7- √6)(√7+ √6)
= (√7+ √6)/((√7)^2-(√6)^2 )
= (√7+ √6)/1
= √7+ √6

Question 4: Represent 5.222222… in a rational form.
Solution:
Let x = 5.2222222...
10x = 52.22222.....
On subtracting 1st equation from the 2nd equation, we get
9x = 47
x = 47/9