Q. 64.0( 6 Votes )

State whether the given statement is true or false.

i. The sum of two rationals is always rational.

ii. The product of two rationals is always rational.

iii. The sum of two irrationals is always an irrational.

iv. The product of two irrationals is always an irrational.

v. The sum of rational and an irrational is irrational.

vi. The product of a rational and an irrational is irrational.

Answer :

i. True ii. True


iii. False iv. False


v. True vi. True


(iii) Let’s take (2 + ) and (2 ‒ ).


These are irrational numbers.


Their sum = (2 + ) + (2 ‒ ) = 4 {which is rational}.


it is false.


(iv) Let’s take (3 + ) and (3 ‒ ).


These are irrational numbers.


Their product = (3 + ) × (3 ‒ ) = 9 + 3√2 – 3√2 – (√2)2


= 9 – 4 = 5 {which is rational}


it is false.


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 LemmaInteractive Quiz:Euclid's Division LemmaInteractive Quiz:Euclid's Division Lemma44 mins
Fundamental Theorem of Arithmetic-2Fundamental Theorem of Arithmetic-2Fundamental Theorem of Arithmetic-238 mins
Champ Quiz | Fundamental Principle Of ArithmeticChamp Quiz | Fundamental Principle Of ArithmeticChamp Quiz | Fundamental Principle Of Arithmetic41 mins
Euclids Division LemmaEuclids Division LemmaEuclids Division Lemma49 mins
Fundamental Theorem of Arithmetic- 1Fundamental Theorem of Arithmetic- 1Fundamental Theorem of Arithmetic- 143 mins
Quiz | Imp Qs on Real NumbersQuiz | Imp Qs on Real NumbersQuiz | Imp Qs on Real Numbers37 mins
NCERT | Imp. Qs. on Rational and Irrational NumbersNCERT | Imp. Qs. on Rational and Irrational NumbersNCERT | Imp. Qs. on Rational and Irrational Numbers44 mins
Relation Between LCM , HCF and NumbersRelation Between LCM , HCF and NumbersRelation Between LCM , HCF and Numbers46 mins
Application of Euclids Division LemmaApplication of Euclids Division LemmaApplication of Euclids Division Lemma50 mins
Quiz | Fun with Fundamental Theorem of ArithmeticQuiz | Fun with Fundamental Theorem of ArithmeticQuiz | Fun with Fundamental Theorem of Arithmetic51 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
caricature
view all courses