# 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.

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 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  Quiz | Imp Qs on Real Numbers37 mins  NCERT | Imp. Qs. on Rational and Irrational Numbers44 mins  Relation Between LCM , HCF and Numbers46 mins  Application of Euclids Division Lemma50 mins  Quiz | 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 view all courses 