Prove that 3 +2√5 is irrational

Prove that 3 +2√5 is irrational

let us assume to the contrary that 3+ 2√5 is a rational number. So

3 + 2√5 = p/q , where p and q are coprime integers and q is not equal to zero

2√5 = p/q -3

2√5 = (p-3q)/q

√5= (p-3q)/2q

since √5 is irrational but (p-3q)/2q is rational.

And rational number can not equal to irrational number. So there is a contradiction. Our assumption is wrong, hence 3+2√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

exercise 1.2 Class 10 Maths | real numbers class 10

 

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

 

Ncert Solutions Class 10 Maths Exercise 2.2

exercise 2.2 class 10 maths | Polynomials class 10 Maths

 

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 Chaptershttps://sharmatutorial.in/category/mcq-class-10-maths/

https://10thmathsguide.com