What number produces an irrational number when multiplied by -1.25

a) square root of 17 when multipled by -1.25

Option 'D' is correct.

Step-by-step explanation:

When a rational number is multiplied by rational number , it gives rational number only.

When an irrational number is multiplied by rational number, it gives irrational number always.

Since we need to produce an irrational number .

A. 3/4 is a rational number if we multiply by -1.25 it will remain a rational number.

B. is a rational number if we multiply by -1.25 it will still remain a rational number.

C. is a rational number if we multiply by -1.25 it will still remain a rational number.

D. square root 17 = √17 is an irrational number if we multiply by -1.25 , it still remain irrational number.

So, Option 'D' is correct.

A rational times an irrational is irrational.

Step-by-step explanation:

Let  x  be an irrational number and

be a rational number

We want to show that is irrational through contradiction:

Assume is rational. Rearranging, we get ;

which is a contradiction.

Therefore, a rational times an irrational is irrational.