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

d. 0

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.
`(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
`(1)/(10)`.

Result is:
`(\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.