Asked by Tony

Which of the following statements is false?

The sum of two rational numbers is always rational.

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

The product of a nonzero rational number and an irrational number is always irrational.

The product of two irrational numbers is either rational or irrational.
Answered by MathMate
"The sum of two rational numbers is always rational." - true, for example, 2+0.5=2.5 (decimals and fractions are rational)
So statement is true.

"The product of a nonzero rational number and an irrational number is always irrational." - true, 5*√2=5(√2) remains irrational. But watch 0*√2=0 (rational). However, 0 is not "nonzero", so the statement remains true.

"The product of two irrational numbers is either rational or irrational." √2*√3=√6 - irrational
√2*√2=√4=2 - rational.
So statement is true.

Finally,
"The sum of a rational number and an irrational number is always rational."
I can easily find examples where the sum of rational and irrational is irrational, as in:
2+√2 : irrational
but unable to find a case where the sum is rational.
Since the statement says "always rational", one single counter-example (as I gave above) invalidates the statement.
Answered by Anonymous
so the answer is D?
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