- Natural and Whole Number
- |
- Integers
- |
- Rational and Irrational Numbers
- |
- Real Numbers
- |
- Laws of exponents
- |
- What is Number Line
- |
- successive Magnification

In this page we have *NCERT Solutions for Class 9th Maths: Chapter 1 NumberSystems * for
Exercise 1.5 and 1.6 . Hope you like them and do not forget to like , social share
and comment at the end of the page.Free download also available

Classify the following numbers as rational or irrational:

(i) 2 - √5

(ii) (3 + √23) - √23

(iii) 2√7/7√7

(iv) 1/√2

(v) 2π

Simplify each of the following expressions:

(i) (3 + √3) (2 + √2)

(ii) (3 + √3) (3 - √3)

(iii) (√5 + √2)

(iv) (√5 - √2) (√5 + √2)

(i) (3 + √3) (2 + √2)

= 3 × 2 + 2 + √3 + 3√2+ √3 ×√2

= 6 + 2√3 +3√2 + √6

(ii) (3 + √3) (3 - √3)

Now as (

= 3

= 9 - 3= 6

(iii) (√5 + √2)

Now as (

= (√5)

= 5 + 2 + 2 × √5× 2

= 7 +2√10

(iv) (√5 - √2) (√5 + √2)

Now as (

= (√5)

= 5 – 2= 3

Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = c/d. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

There is no contradiction. When we measure a value with a scale, we only obtain an approximate value. We never obtain an exact value. Therefore, we may not realize that either c or d is irrational. The value of π is almost equal to 22/7 or 3.142857...

Represent √9.3 on the number line.

Rationalize the denominators of the following:

(i) 1/√7

(ii) 1/ (√7-√6)

(iii) 1/ (√5+√2)

(iv) 1/ (√7-2)

Find:

(i) 64

(ii) 32

(iii) 125

i) 64

ii) 32

iii) 125

Find:

(i) 9

(ii) 32

(iii) 16

(iv) 125

i) 9

ii) 32

iii) 16

iv) 125

Simplify:

(i) 2

(ii) (1/3

(iii) 11

(iv) 7

i) 2

ii) (1/3

=1/3

iii) 11

= 11

iv) 7

=(7X8)

Download Number System NCERT Solutions 1.5 and 1.6 as pdf

Given below are the links of some of the reference books for class 9 Math.

- Mathematics for Class 9 by R D Sharma One of the best book for studying class 9 level mathematics. It has lot of problems to be solved.
- Secondary School Mathematics for Class 9 by R S Aggarwal This is also as good as R.D. Sharma. Either this or the book by R.D. Sharma will do. I find book R.S. Aggarwal little bit more challenging than the one by R.D. Sharma.
- Pearson IIT Foundation Series - Maths - Class 9 Buy this book if you want to challenge yourself further and want to prepare for JEE foundation.
- Pearson IIT Foundation Physics, Chemistry & Maths combo for Class 9 Only buy if you are prepared to study extra topics and want to take your studies a step further. You might need help to understand topics in these books.

You can use above books for extra knowledge and practicing different questions.

Class 9 Maths Class 9 Science

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