Which of the following statement is false

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

Step-by-step explanation:

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

For Example: 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: 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 , 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.

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step-by-step explanation: