The square roots of 2 and 3 are irrational but not transcendent.
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No, 3 is a rational number. Pi and the square root of 2 are irrational numbers.
It is irrational.
sqrt(2) is irrational. 3 is rational. The product of an irrational and a non-zero rational is irrational. A more fundamental proof would follow the lines of the proof that sqrt(2) is irrational.
They are rational.
Yes, numbers fall into two categories rational and irrational. Rational: Fractions Terminating Decimals Integers Irrational: Pi The square root of 2 The square root of 3 Infinity