Question

Which of the following statements is false?

A)The product of two rational numbers is always irrational.
B)The sum of a rational number and an irrational number is always irrational.
C)The product of a nonzero rational number and an irrational number is always irrational.
D)The product of two irrational numbers is either rational or irrational.

Answer 1

A.

Explanation:

So if you do √25*√49 is 13.2287565553

which is irrational but if you do 53 times 53 you get 2809 which is rational so you its Not always irrational

Answer 2

Answer is statement A.

Product of 2 rational number is always rational. Rational number is number which can be represented as ratio which both numerator and denominator are finite whole numbers. If you multiply 2 finite numbers you wiill get 2 finite numbers.

B is true because infinite + finite is infinite (talking about numerators)

C simillar case as B. infinite * finite is infinite

D is true as well. for example √2*√2 is rational number. it is number 2. while √2*√3 is irational.