Answered

If x/y

is rational, must x and y each be rational?

AYes; because the quotient of rationals is rational.
BNo; because x and y could have a common irrational factor.
CNo; because the quotient of irrationals is always irrational.
DYes; because x and y must be integers, and integers are rational.

Verified Answer :

masonmb

The answer is B.

Consider the fraction \(\frac{6 \sqrt{5} }{\sqrt{5}}\).

Both the numerator and denominator, when by themselves, are irrational.

However, when they are divided, they result in the rational number \(\frac{6 \sqrt{5} }{\sqrt{5}}=\boxed{6}\).

When \(p,q\) have the same irrational factor, the irrational factor will be cancelled from the fraction and (possibly) leave a rational number.


travinator305

Answer: The answer is B.


Step-by-step explanation:

No; because x and y could have a common irrational factor.

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