Q. 5 A5.0( 3 Votes )

# Prove that following numbers are irrational :

6 + √2

Answer :

Let us assume 6 + is rational

6 + can be written in the form where a and b are co-prime.

Hence, 6 + =

= – 6

=

=

Since, rational ≠ irrational

This is a contradiction.

, Our assumption is incorrect.

Hence, 6 + 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

Champ Quiz | Fundamental Principle Of Arithmetic41 mins

Euclids Division Lemma49 mins

Fundamental Theorem of Arithmetic- 143 mins

NCERT | Imp. Qs. on Rational and Irrational Numbers44 mins

Quiz | Imp Qs on Real Numbers37 mins

Application of Euclids Division Lemma50 mins

Relation Between LCM , HCF and Numbers46 mins

Quiz | Fun with Fundamental Theorem of Arithmetic51 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

RELATED QUESTIONS :

Prove that following numbers are irrational :

√3 – √2

KC Sinha - MathematicsProve that following numbers are irrational :

5 – √3

KC Sinha - MathematicsProve that following numbers are not rational :

5√3

KC Sinha - Mathematics