Question

chris is multiplying an irrational number m by a rational number k. the product is a rational number. what is the value of k? select one answer a ( k = -m ) b ( k = 1 ) c ( k = 0 ) d ( k = m )

Explanation:

Step1: Recall rational/irrational properties

An irrational number $m$ cannot be written as $\frac{a}{b}$ where $a,b$ are integers, $b
eq0$. A rational number $k$ can be written as $\frac{c}{d}$ where $c,d$ are integers, $d
eq0$.

Step2: Test option A

$k=-m$: $m$ is irrational, so $-m$ is irrational, violates $k$ rational.

Step3: Test option B

$k=1$: Product is $1\times m = m$, which is irrational, contradicts given product rational.

Step4: Test option C

$k=0$: Product is $0\times m = 0$, which is rational ($0=\frac{0}{1}$), satisfies all conditions.

Step5: Test option D

$k=m$: $m$ is irrational, so $k$ is irrational, violates $k$ rational.

Answer:

C. $k=0$