Answer:
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: [tex]\dfrac{2}{7} + (-5)= \dfrac{-33}{7}[/tex] 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: [tex]\frac{2}{3 } +\sqrt{3}[/tex] 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 [tex]\frac{p}{q}[/tex], 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.
