Question

I really stuck on this question can someone help me out? What rational number, when multiplied by an irrational number, has a product that is a rational number? a. 1/2 b. 1 c. 1/10 d. 0

Answer 1

Answer:

d. 0

Step-by-step explanation:

Given that:

A rational number is multiplied by a irrational number.

And the result is a rational number.

To find:

Such rational number wil be:

a. $\frac{1}2$

b. 1

c. $\frac{1}{10 }$

d. 0

Solution:

Let us consider the given options one by one.

Let the irrational number be = $\pi$

Checking option a.

Multiply $\pi$ and $\frac{1}2$.

Result is: $\frac{\pi}2$ which is again irrational.

So, a. is not correct.

Checking option b.

Multiply $\pi$ and 1.

Result is: $\pi$ which is again irrational.

So, b. is not correct.

Checking option a.

Multiply $\pi$ and $\frac{1}{10}$.

Result is: $\frac{\pi}{10}$ which is again irrational.

So, c. is not correct.

Checking option d.

Multiply $\pi$ and 0.

Result is: 0 which is rational.

So, d. 0 is the correct answer.