Question

Select from the drop-down menus to correctly complete the proof.

Answer 1

rational irrational irrational

Answer 2

Answer: Rational, irrational and irrational are the right options.

Explanation:  

Given Number= 3√12

We have to prove that 3√12 is a irrational number.  

let us assume 3√12 is a rational number.

Since, we can write, 3√12=3×2×√3=6√3

⇒ Right side(that is 6) is rational but the left side(that is √3) is irrational which is a contradiction(because, rational number is always the product of rational number and product of a rational number and an irrational number is always an irrational number.)

Therefore, the assumption is wrong, and the product is irrational.