Question

Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:
(i)√4 (ii) 3√18 (iii) √1.44 (iv) √(9/27)(v) -√64 (vi) √100

Answer 1

(i) Given :  √4

√4 = 2, which can be written in the form of p/q. Therefore, it is a rational number.

Its decimal representation is 2.0.

 

(ii) Given : 3√18

3√18 = 3√(9 × 2) = 3 × 3√2 = 9√2

We know that, the product of a rational and an irrational number is an irrational number.

Therefore, 3√18 is an irrational number.

 

(iii) Given : √1.44

√1.44 = 1.2

Since, every terminating decimal is a rational number, Therefore, √1.44 is a rational number.

Its decimal representation is 1.2.

 

(iv) Given : √(9/27)

√9/27 = √(⅓) = 1/√3

Since, we know, quotient of a rational and an irrational number is an irrational number. Therefore, √9/27 is an irrational number.

(v) Given :  – √64

– √64 = – 8 = – 8/1

Therefore, – √64 is a rational number.

Its decimal representation is – 8.0.

 

(vi) Given : √100

√100 = 10

Since, 10 can be expressed in the form of p/q such as 10/1,

Therefore, √100 is a rational number.

It’s decimal representation is 10.0.

HOPE THIS ANSWER WILL HELP YOU…..

Similar questions :

Examine, whether the following numbers are rational or irrational: (i) √7 (ii)√4 (iii) 2+√3(iv) √3+√4 (v) √3+√5 (vi) (√2-2)² (vii) (2-√2) (2+√2) (viii)(√2+√3)² (ix) √5-2 (x)√23 (xi) √225 (xii) 0.3796 (xiii) 7.478478 (xiv) 1.101001000100001…..

https://brainly.in/question/15896920

Give an example of each, of two irrational numbers whose:

(i) Difference is a rational number.

(ii) Difference is an irrational number.

(iii) Sum is a rational number.

(iv) Sum is an irrational number.

(v) Product is a rational number.

(vi) Product is an irrational number.

(vii) Quotient is a rational number.

(viii) Quotient is an irrational number.

https://brainly.in/question/15896923

Answer 2

(1) √4 = 2

Thus, it is a rational number.

Representation: 2.0

(2) 3√18 = 3√2×3×3 = 9√2

Thus, since √2 is irrational, its an irrational number

(3) √1.44 = 1.2

Thus, its a rational number

Representation: 1.20

(4) √(9/27) = 3/3√3 = 1/√3

Thus, since √3 is irrational, its an irrational number

(5) -√64 = -8

Since -8 is a real number, It's a rational number

Representation: -8.0

(6) √100 = 10

Since 10 is a real number and can be represented in the form p/q, it is a rational number

Representation: 10.0