Answer :

Let k = is rational

k – 1 =


(k – 1)2 = 2


k2 + 1–2k = 3 + 2 + 2


k2–2k = 5 – 1 + 2


k2–2k = 4 + 2 is rational


= is rational


But, we know that is irrational.


So, our assumption is wrong.


Therefore, + + 1 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
Interactive Quiz:Euclid's Division Lemma44 mins
Fundamental Theorem of Arithmetic-238 mins
Fundamental Theorem of Arithmetic- 143 mins
Champ Quiz | Fundamental Principle Of Arithmetic41 mins
NCERT | Imp. Qs. on Rational and Irrational Numbers44 mins
Euclids Division Lemma49 mins
Quiz | Imp Qs on Real Numbers37 mins
Interactive Quiz - HCF and LCM32 mins
Application of Euclids Division Lemma50 mins
Relation Between LCM , HCF and Numbers46 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
RELATED QUESTIONS :

Prove is irrational.

Gujarat Board Mathematics

√4 + 3 is……..

Gujarat Board Mathematics

Simplify :

Gujarat Board Mathematics

Simplify :

Gujarat Board Mathematics