Question

Which of the following statement is false

Answer 1

I believe the answer would be C. The product of a nonzero rational number and an irrational number is always irrational

Answer 2

B. The sum of a rational number and an irrational number is always rational.

Explanation:

A. Yes, The sum of two rational numbers is rational.

For Example:
`(2)/(7) + (-5)= (-33)/(7)` which is again a rational number. Thus, this is true.

B. No, The sum of a rational number and an irrational number is always irrational.

Example:
`(2)/(3 ) +√(3)` is a rational number. Hence, given statement is false.

C. Yes, The product of a non-zero rational number and an irrational number is always an irrational number.

Example: 2 × √5 = 2√5 which is an irrational number. Thus, it is also the correct statement.

D. Yes, the product of two irrational numbers is either rational or irrational number.

For Example: √2 × √2 = 2 which is a rational number.

But, √2 × √3 = √6 which is an irrational number.

Thus, this statement is also true.

Further,

Rational Number: The number that can be changed in the form of
`(p)/(q)`, where p and q are integers and q ≠ 0.

Irrational Number: The numbers which are not rational are called irrational number. Further, all non-terminating, non-repeating decimals are an irrational number.