Question

which of the following is an irrational number? 1) 169 2) 3.3535.... 3) 0.5 4) 2.1010010001...​

Answer 1

number 2 and number 4 are irrational numbers

Answer 2

Given : 1) 169 2) 3.3535.... 3) 0.5 4) 2.1010010001...​

To Find : an irrational number

Solution:

Real numbers can be categorized in

rational numbers and irrational numbers

Rational numbers can be written in the form

p/q where p and q are integers and q ≠ 0

These can be terminating decimal

or non terminating  recurring decimals

which are not rational are irrational

and these are non terminating non recurring decimals

169 = 169/1   Rational

0.5 = 5/10 = 1/2  Rational

N = 3.3535...

100N = 335.3535...

=> 99N  = 332

=> N = 332/99 Rational

2.1010010001...​  non terminating non recurring decimals

Hence IRRATIONAL

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