Q. 64.3( 3 Votes )
You have seen that √2 is not a rational number. Show that
2 + √2 is not a rational number.
Answer :
Let 2 + √2be a rational number say r.
Then,2 + √2=r
√2=r - 2
But, √2is an irrational number.
LHS is irrational thus RHS should also be irrational to maintain the equality.
Therefore, r – 2 is also an irrational number
⇒ r is an irrational number.
Hence our assumption r is a rational number is wrong.
Hence, 2 + √2 is not a rational number.
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
PREVIOUSWhich of the following rational numbers have the terminating decimalrepresentation? (i)3/5 (ii)7/20 (iii)2/13 (iv) 27/40 (v)133/125 (vi)23/7 [Making use of the result that a rational number p/q where p and q have nocommon factor(s) will have a terminating representation if and only if theprime factors of q are 2's or 5's or both.NEXT Prove that Prove that3â3is not a rational number.
Related Videos
Interactive Quiz:Euclid's Division Lemma44 mins
Fundamental Theorem of Arithmetic-238 mins
Fundamental Theorem of Arithmetic- 143 mins
NCERT | Imp. Qs. on Rational and Irrational Numbers44 mins
Champ Quiz | Fundamental Principle Of Arithmetic41 mins
Euclids Division Lemma49 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
Interactive Quiz:Euclid's Division Lemma44 minsFundamental Theorem of Arithmetic-238 minsFundamental Theorem of Arithmetic- 143 minsNCERT | Imp. Qs. on Rational and Irrational Numbers44 minsChamp Quiz | Fundamental Principle Of Arithmetic41 minsEuclids Division Lemma49 minsQuiz | Imp Qs on Real Numbers37 minsApplication of Euclids Division Lemma50 minsRelation Between LCM , HCF and Numbers46 minsQuiz | Fun with Fundamental Theorem of Arithmetic51 minsTry our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
view all courses
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
RELATED QUESTIONS :
Draw the graph of 2x – 3y = 4. From the graph, find whether x = -1, y = -2 is a solution or not. (Final)
NCERT - MathematicsProve the following identities :
tan4θ + tan2θ = sec4θ – sec2θ
KC Sinha - MathematicsIf
, then find the values of sin θ and cos θ.
Write the first three terms of the following sequences defined by:
