Question

identify the following as rational or irrational numbers. give decimal representation of rational numbers:
1. 3 root18
2. root1.44
3.-root64
4. root9/27

Answer 1

1.) 3√18
3√2×3²
9√2 ....(Rational× Irrational= IrRational)
2.) √1.44 Irrational
3.) √-64 Complex
4.) √9/27= 3/27= 1/9 Rational
Decimal Expansion= 0.11

Answer 2

$\sf \underline \red{Solution:}$

(i) 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 × √18 is an irrational number.

(ii) √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

(iii) – √64

– √64 = – 8 or – 8/1

Therefore, – √64 is a rational number.

Its decimal representation is –8.0

(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.

$\sf \purple{Thanks}$