Identify the following as rational or irrational numbers. Give the dec

1.	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» (i) √4 √4 = 2, which can be written in the form of a/b. Therefore, it is a rational number. Its decimal representation is 2.0. (ii) 3√18 3√18 = 9√2 Since, the product of a rational and an irrational number is an irrational number. Therefore, 3√18 is an irrational. Or 3 x √18 is an irrational number. (iii) √1.44 √1.44 = 1.2 Since, every terminating decimal is a rational number, Therefore, √1.44 is a rational number. And, its decimal representation is 1.2. (iv) √9/27 √9/27 = 1/√3 Since, we know, quotient of a rational and an irrational number is irrational numbers, therefore, √9/27 is an irrational number. (v) – √64 – √64 = – 8 or – 8/1 Therefore, – √64 is a rational number. Its decimal representation is –8.0. (vi) √100 √100 = 10 Since, 10 can be expressed in the form of a/b, such as 10/1, Therefore, √100 is a rational number. And it’s decimal representation is 10.0.

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»

(i) √4

√4 = 2, which can be written in the form of a/b. Therefore, it is a rational number. Its decimal representation is 2.0.

(ii) 3√18

3√18 = 9√2

Since, the product of a rational and an irrational number is an irrational number.

Therefore, 3√18 is an irrational.

Or 3 x √18 is an irrational number.

(iii) √1.44

√1.44 = 1.2

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

And, its decimal representation is 1.2.

(iv) √9/27

√9/27 = 1/√3

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

(v) – √64

– √64 = – 8 or – 8/1

Therefore, – √64 is a rational number.

Its decimal representation is –8.0.

(vi) √100

√100 = 10

Since, 10 can be expressed in the form of a/b, such as 10/1,

Therefore, √100 is a rational number.

And it’s decimal representation is 10.0.