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Only if the rational number is 0.

Q: Can a rational number be multiplied by an irrational number and equal a rational number?

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It can be a rational number or an irrational number. For example, sqrt(2)*sqrt(50) = 10 is rational. sqrt(2)*sqrt(51) = sqrt(102) is irrational.

No.

The sum 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.

Yes, it will always be irrational.

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An irrational number is a number that has no definite end. So it can't be multiplied or divided by anything to make a rational number that does have a definite end.

It can be a rational number or an irrational number. For example, sqrt(2)*sqrt(50) = 10 is rational. sqrt(2)*sqrt(51) = sqrt(102) is irrational.

No.

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

The sum 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.

Yes

Yes, it will always be irrational.

No, never.

Yes, always.

The product of two irrational numbers may be rational or irrational. For example, sqrt(2) is irrational, and sqrt(2)*sqrt(2) = 2, a rational number. On the other hand, (2^(1/4)) * (2^(1/4)) = 2^(1/2) = sqrt(2), so here two irrational numbers multiply to give an irrational number.

from another wikianswers page: say that 'a' is rational, and that 'b' is irrational. assume that a + b equals a rational number, called c. so a + b = c subtract a from both sides. you get b = c - a. but c - a is a rational number subtracted from a rational number, which should equal another rational number. However, b is an irrational number in our equation, so our assumption that a + b equals a rational number must be wrong.