Q. 14.6( 18 Votes )

Let us write the right or False statement from the following:

(i) The sum of two rational numbers will always be rational.

(ii) The sum of two irrational numbers will always be irrational.

(iii) The product of two rational numbers will always be rational.

(iv) The product of two irrational numbers will always be rational.

(v) Each rational number must be real.

(vi) Each real number must be irrational.

Answer :

(i) True


We can explain this with an example.


Let the two rational numbers be and .


On addition, which is also a rational number.


(ii) True


We can explain this with an example.


Let the two irrational numbers be √2 and √3


On addition, √2+√3, which is also an irrational number.


(iii) True


Explanation: We can explain this with an example.


Let the two rational numbers be and .


On addition, which is also a rational number.


(iv) False


We can explain this with an example.


Let the two irrational numbers be √3 and √5


On multiplication, √3 × √5 = √15,


which is an irrational number. So, this is not always true.


(v) True


Since a rational number can be plotted on a number line, therefore, every rational number is a real number.


(vi) False


This can be explained with an example. Let us consider any real number, say 2, 2 is a real number as it can be plotted on a number line.


We can write 2 as , so 2 is a rational number.


The given statement is not always true.


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