# NumberSystems Exercise 1.5 and 1.6|NCERT Solutions for Class 9th Maths

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

## 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
= 32 - (√3)2
= 9 - 3= 6
(iii) (√5 + √2)
Now as (a + b)2 = a2 + b2 + 2ab
= (√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) 641/2
(ii) 321/5
(iii) 1251/3
Solution
i) 641/2 =(26)1/2  =26 X1/2  = 23 =8
ii) 321/5  =(25)1/5 = 2
iii) 1251/3 = (53)1/3 =5
Question 2
Find:
(i) 93/2
(ii) 322/5
(iii) 163/4
(iv) 125-1/3
Solution
i) 93/2 = (32)3/2 = 27
ii) 322/5 = (25)2/5 =4
iii) 163/4 = (24)3/4 =8
iv) 125-1/3 = 1/1251/3 = 1/(53)1/3 =1/5
Question 3.
Simplify:
(i) 22/3.21/5
(ii) (1/33)7
(iii) 111/2/111/4
(iv) 71/2.81/2

Solution
i) 22/3.21/5 =2 2/3+ 1/5 = 210+3/15 =213/15
ii) (1/33)7
=1/33X7 = 1/321 =3 -21
iii) 111/2/111/4
= 111/2 -1/4  = 111/4
iv) 71/2.81/2
=(7X8)1/2 = 561/2