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That ain't necessarily true in all cases. For example, square root of 2 Times Square root of 2 is equal to two, which is RATIONAL.

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Q: Why does a nonzero number times an irrational number eaqual an iraational number?

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It is irrational.

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)

An irrational number.

It is an irrational number.

It is always irrational.

Yes.

Yes, always.

The product will be irrational.

Yes, always.

It means that: a) The number is irragional, and b) the number is not zero. Since zero is rational, it isn't irrational, so saying that it is nonzero is really superfluous.

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The product of an irrational number and a rational number, both nonzero, is always irrational