Q3 of 96 Page 6

State whether the following statements are true or false? Justify your answer.

is a rational number.

False

is not a rational number.


Justification: We can write as .


Here, √2 is irrational and 1/3 is rational number.


Product of a rational and an irrational number is always irrational.


∴ is irrational.


Hence, it is not rational and thus the given statement is false.


More from this chapter

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1

Let x and y be rational and irrational numbers, respectively. Is x + y necessarily an irrational number? Give an example in support of your answer.

 2

Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example.

 3

State whether the following statements are true or false? Justify your answer.

There are infinitely many integers between any two integers.

 3

State whether the following statements are true or false? Justify your answer.

Number of rational numbers between 15 and 18 is finite.