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
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Exercise 1.5
Question 1
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
Solution
Question 2
Simplify each of the following expressions:
(i) (3 + √3) (2 + √2)
(ii) (3 + √3) (3 - √3)
(iii) (√5 + √2)
2
(iv) (√5 - √2) (√5 + √2)
Solution
(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 (
a +
b) (
a -
b) =
a2 -
b2
= 3
2 - (√3)
2
= 9 - 3= 6
(iii) (√5 + √2)
2
Now as (
a +
b)
2 =
a2 +
b2 + 2
ab
= (√5)
2 + (√2)
2 + 2 ×√5 × √2
= 5 + 2 + 2 × √5× 2
= 7 +2√10
(iv) (√5 - √2) (√5 + √2)
Now as (
a +
b) (
a -
b) =
a2 -
b2
= (√5)
2 - (√2)
2
= 5 – 2= 3
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 = c/d. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
Solution
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...
Question 4.
Represent √9.3 on the number line.
Question 5
Rationalize the denominators of the following:
(i) 1/√7
(ii) 1/ (√7-√6)
(iii) 1/ (√5+√2)
(iv) 1/ (√7-2)
Solution
Exercise 1.6
Question 1.
Find:
(i) 64
1/2
(ii) 32
1/5
(iii) 125
1/3
Solution
i) 64
1/2 =(2
6)
1/2 =2
6 X1/2 = 2
3 =8
ii) 32
1/5 =(2
5)
1/5 = 2
iii) 125
1/3 = (5
3)
1/3 =5
Question 2
Find:
(i) 9
3/2
(ii) 32
2/5
(iii) 16
3/4
(iv) 125
-1/3
Solution
i) 9
3/2 = (3
2)
3/2 = 27
ii) 32
2/5 = (2
5)
2/5 =4
iii) 16
3/4 = (2
4)
3/4 =8
iv) 125
-1/3 = 1/125
1/3 = 1/(5
3)
1/3 =1/5
Question 3.
Simplify:
(i) 2
2/3.2
1/5
(ii) (1/3
3)
7
(iii) 11
1/2/11
1/4
(iv) 7
1/2.8
1/2
Solution
i) 2
2/3.2
1/5 =2
2/3+ 1/5 = 2
10+3/15 =2
13/15
ii) (1/3
3)
7
=1/3
3X7 = 1/3
21 =3
-21
iii) 11
1/2/11
1/4
= 11
1/2 -1/4 = 11
1/4
iv) 7
1/2.8
1/2
=(7X8)
1/2 = 56
1/2
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Class 9 Maths
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