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To prove that 3√⋅12 is irrational, assume the product is rational and set it equal to ​ ab ​, where b is not equal to 0. Isolating the radical gives 3√=2ab . The right side of the equation is (irrational, rational). Because the left side of the equation is (irrational, rational) , this is a contradiction. Therefore, the assumption is wrong, and the product is (irrational, rational) .

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ArmanaLaRana

rational irrational irrational

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.

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