Q. 64.3( 6 Votes )

State in each case, whether the given statement is true or false.

(i) The sum of two rational numbers is rational.

(ii) The sum of two irrational numbers is irrational.

(iii) The product of two rational numbers is rational.

(iv) The product of two irrational numbers is irrational.

(v)The sum of a rational number and an irrational number is irrational.

(vi) The product of a nonzero rational number and an irrational number is a rational number.

(vii)Every real number is rational.

(viii) Every real number is either rational or irrational.

(ix) is irrational and is rational.

Answer :

(i) True: = always a rational number.


(ii) False: = , which is a rational number.


(iii) True: = always a rational number.


(iv) False: = which is a rational number.


(v) True : = , is always irrational.


(vi) False: = is always an irrational number.


(vii) False : As rational numbers are on number line and all numbers on number line is real. Hence, every rational number is also Real.


(viii) True: As both rational and irrational numbers can be presented at number line are real. Hence they may be rational or irrational.


(ix) True: π = 3.141592653…… non terminating decimal form and is a fractional form.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Number SystemsChamp Quiz | Number SystemsChamp Quiz | Number Systems43 mins
Genius Quiz | Number SeriesGenius Quiz | Number SeriesGenius Quiz | Number Series24 mins
Simplification of Expressions and Finding their Values Using Laws of ExponentsSimplification of Expressions and Finding their Values Using Laws of ExponentsSimplification of Expressions and Finding their Values Using Laws of Exponents38 mins
Score more on Number lineScore more on Number lineScore more on Number line44 mins
Irrational numbers on Number lineIrrational numbers on Number lineIrrational numbers on Number line32 mins
Terminating & Non - Terminating Decimal ExpansionTerminating & Non - Terminating Decimal ExpansionTerminating & Non - Terminating Decimal Expansion51 mins
The Curious Case of Irrational NumbersThe Curious Case of Irrational NumbersThe Curious Case of Irrational Numbers43 mins
Doubts & Quiz - Simplification of Expressions and Laws of ExponentsDoubts & Quiz - Simplification of Expressions and Laws of ExponentsDoubts & Quiz - Simplification of Expressions and Laws of Exponents41 mins
Bonus Questions on RationalizationBonus Questions on RationalizationBonus Questions on Rationalization47 mins
Quiz on Irrational NumbersQuiz on Irrational NumbersQuiz on Irrational Numbers31 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
RELATED QUESTIONS :

The number expressed as a vulgar fraction is

RS Aggarwal & V Aggarwal - Mathematics

The simplest form of

RS Aggarwal & V Aggarwal - Mathematics

28. The simplest form of is

RS Aggarwal & V Aggarwal - Mathematics

The simplest form of

RS Aggarwal & V Aggarwal - Mathematics

The simplest form of

RS Aggarwal & V Aggarwal - Mathematics