# Class 9 maths chapter 1 exercise 1.5 and 1.6 solutions

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## Class 9 maths chapter 1 exercise 1.5 solutions

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

## Class 9 maths chapter 1 exercise 1.6 solutions

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

## Summary

1. Class 9 maths chapter 1 exercise 1.5 solutions and Class 9 maths chapter 1 exercise 1.6 solutions has been prepared by Expert with utmost care. If you find any mistake.Please do provide feedback on mail. You can download the solutions as PDF in the below Link also
Download Number System NCERT Solutions 1.5 and 1.6 as pdf
2. This chapter 1 has total 6 Exercise 1.1 ,1.2,1.3 ,1.4 ,1.5 and 1.6. This is the Fifth and Sixth exercise in the chapter.You can explore previous exercise of this chapter by clicking the link below