Q. 95.0( 1 Vote )

Identify the following as rational or irrational numbers. Give the decimalrepresentation of rational numbers.
(i)√4
(ii) 3√18
(iii)√1.44
(iv)

(v) -√0.64
(vi) √100

Answer :


(i) Given:√4

√4=2

2=2/1

It can be represented in form p/q (p=2, q=1) where q≠0 and p;q have no common factor other than 1.

Hence √4 is a rational number.

(ii)Given: 3√18

3√18=3√(9×2)= 3√3 2 ×2

3×3√2=9√2

(value of √2 =1.4142135623…)

=9×1.4142135623…

=12.72792206135…

It cannot be represented in form p/q and is non terminating and non repeating.

Hence 3√18 is an irrational number.

The decimal representation of 3√18 is 12.72792206135…

(iii) Given √1.44

Now,

It can be represented in form p/q (p=6, q=5) where q≠0 and p;q have no common factor other than 1.

Hence √1.44 is rational number.

The decimal representation of √1.44 is 1.2 (12/10).

(iii) Given:

It cannot be expressed as ratio of two integers and value of √3 = 1.7320508075688… which is non-termination non repeating.

Hence, is an irrational number.

(Rationalising by √3)

=0.57735

The decimal representation of is 0.57735

(v)

Now,

It can be represented in form p/q (p=4, q=5) where q≠0 and p;q have no common factor other than 1.

Hence, is rational number.

The decimal representation of -√0.64 is -0.8

(vi) √100= √10×10 = 10

=10/1

It can be represented in form p/q (p=10, q=1) where q≠0 and p;q have no common factor other than 1.

Hence √100 is a rational number.

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