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Is 
sqrt2*sqrt3 rational or irrational?
Choose 1 answer:
(A) Rational
(B) Irrational
(C) It can be either rational or irrational

Is 23\sqrt{2}\cdot\sqrt{3} rational or irrational?\newlineChoose 11 answer:\newline(A) Rational\newline(B) Irrational\newline(C) It can be either rational or irrational

Full solution

Q. Is 23\sqrt{2}\cdot\sqrt{3} rational or irrational?\newlineChoose 11 answer:\newline(A) Rational\newline(B) Irrational\newline(C) It can be either rational or irrational
  1. Evaluate Product of Square Roots: Evaluate the product of 2\sqrt{2} and 3\sqrt{3}.2×3=2×3\sqrt{2} \times \sqrt{3} = \sqrt{2 \times 3}=6= \sqrt{6}
  2. Identify Rationality of 6\sqrt{6}: Identify whether 6\sqrt{6} is a rational or irrational number.\newline6\sqrt{6} is not a perfect square, and cannot be simplified to a fraction of integers.\newlineTherefore, 6\sqrt{6} is an irrational number.

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