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Q: Is three times an irrational number always an irrational number?

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No.A rational times an irrational is never rational. It is always irrational.

The square root of 2 is irrational, yet the product of it with itself is 2. So the answer is no.

No. If the rational number is not zero, then such a product is irrational.

The product of 0 and an irrational is 0 (a rational), the product of a non-zero rational and any irrational is always irrational.

Not always. For example sqrt(2) and 1/sqrt(2) are both irrational, but their product is the rational number 1.

Actually the product of a nonzero rational number and another rational number will always be rational.The product of a nonzero rational number and an IRrational number will always be irrational. (You have to include the "nonzero" caveat because zero times an irrational number is zero, which is rational)

Not necessarily. 0 times any irrational number is 0 - which is rational.

The square root of 2 times the square root of 2 is rational.

Unless the rational number is zero, the answer is irrational.

There cannot be a proof since your assertion is not necessarily true. sqrt(2)*sqrt(3) = sqrt(6). All three are irrational numbers.

At least one of the factors has to be irrational.* An irrational number times ANY number (except zero) is irrational. * The product of two irrational numbers can be either rational or irrational.

Yes. For example, the square root of 3 (an irrational number) times the square root of 2(an irrational number) gets you the square root of 6(an irrational number)

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