# Find which numbers of the following numbers are rational and which numbers are irrational.i. √23ii. √225iii. 0.3797iv. 7.4784478….v. 1.101001000100001…..

Rational numbers are the numbers which can be expressed in p/q form or simply which have a terminating or repeating decimal expansion.

On the other hand, irrational numbers are the numbers with non repeating and non terminating decimal expansion.

i. √23

Since 23 can’t be expressed as any number’s perfect square.

23 is irrational.

ii. √225

Since 152 = 225

√225 = √152 = 15

√225 is rational.

iii. 0.3797

Since 0.3797 is terminating and non-repeating and can be expressed in the form of

0.3797 is rational

iv. 7.4784478….

Since 7.4784478… is non-terminating and cannot be expressed in the form of

7.4784478…. is irrational

v. 1.101001000100001…..

Since 1.101001000100001….. is non-terminating and cannot be expressed in the form of

1.101001000100001… is irrational

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Rationalizing the Denominator39 mins
The Curious Case of Irrational Numbers43 mins
Irrational numbers on Number line32 mins
Terminating & Non - Terminating Decimal Expansion51 mins
Quiz on Irrational Numbers31 mins
Quiz | Learning the Laws of Exponents52 mins
Quiz | Irrational Numbers and its Operations45 mins
Champ Quiz | Rationalization30 mins
RD Sharma | Practice Imp.Qs. on Number System48 mins
Quiz | Decimals - Whether Rational or Irrational43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses