Best Answer

No.

The easiest counter-example to show that the product of two Irrational Numbers can be a rational number is that the product of √2 and √2 is 2.

Likewise, the cube root of 2 is also an irrational number, but the product of 3√2, 3√2 and 3√2 is 2.

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Q: Is the product of three irrational numbers always an irrational number?

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The product of two rational number is always rational.

No. 0 is a rational number and the product of 0 and any irrational number will be 0, a rational. Otherwise, though, the product will always be irrational.

The product of two rational numbers, as in this example, is always RATIONAL.However, if you mean 10 x pi, pi is irrational; the product of a rational and an irrational number is ALWAYS IRRATIONAL, except for the special case in which the rational number is zero.

Such a product is always irrational - unless the rational number happens to be zero.

It is always irrational.

Not if the rational number is zero. In all other cases, the product is irrational.

The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.

It is always an irrational number.

Yes, always.

sqrt(2)*sqrt(3) is an irrational product.

Provided that the rational number is not 0, the product is irrational.

Yes.

Yes, always.

No, numbers less than 0.833 are not always irrational. For instance, 0.2 isn't an irrational number

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

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

No. The square root of two is an irrational number. If you multiply the square root of two by the square root of two, you get two which is a rational number.

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

No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).

No, but the only exception is if the rational number is zero.

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)

It is always true.

Whole numbers can never be irrational.

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

no x² is the product of 2 rational numbers in this case the same 2 numbers x and x The product of two rational numbers is always rational.