## Prove that √5 is irrational

Sol. Let us assume to the contrary that √5 is an irrational number. So it can be written in the form of p/q where p and q are co-prime integers and q is not equal to zero.

√5= p/q

squaring both sides

(√5)² = (p/q)²

5= p²/q²

p²= 5 q² ,

so p² is divisible by 5 hence p is also divisible by 5. So put p = 5 m in above equation where m is some positive integer.

(5 m)² = 5q²

25 m² = 5q²

q²= 5 m² , so q² is divisible by 5 hence q is also divisible by 5. It means p and q both are divisible by 5. Hence 5 is common factor of p and q. But it contradicts that p and q are co-prime. Therefore our assumption is wrong. Hence √5 is irrational.

Ncert Solutions Class 10 Maths Exercise 1.1 https://10thmathsguide.com/exercise-11-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 1.2

Ncert Solutions Class 10 Maths Exercise 2.1 https://10thmathsguide.com/exercise-21-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 2.2

Ncert Solutions Class 10 Maths Exercise 3.1 https://10thmathsguide.com/exercise-31-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.2 https://10thmathsguide.com/exercise-32-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.3 https://10thmathsguide.com/exercise-33-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.1 https://10thmathsguide.com/exercise-41-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.2 https://10thmathsguide.com/exercise-42-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.3 https://10thmathsguide.com/exercise-43-class-10-maths/

MCQ VIDEOS ALL CHAPTERS CLASS 10 MATHShttps://www.youtube.com/watch?v=-eBlHyBxjLg&list=PL2uPMjJCHErQZZNipbsnagBqPrCU_WRN8

**MCQ Questions for Class 10 Maths all Chapters****https://sharmatutorial.in/category/mcq-class-10-maths/**