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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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โˆ™ 2010-01-19 09:13:21
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Algebra

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A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common factor A True B False

The sum or difference of p and q is the of the x-term in the trinomial

A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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

Is the product of two rational numbers irrational?

The product of two rational number is always rational.


Is the product of a rational number and an irrational number always irrational?

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.


Is 10x 3.14 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.


Is the product of a rational number and an irrational number rational or irrational?

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


Is the product of a nonzero rational number and an irrational number rational or irrational?

It is always irrational.


Is the product of an irrational number and a rational number always an irrational number?

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


What is the product of rational and irrational number?

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


The sum of rational numbers and an irrational number?

It is always an irrational number.


Is the product of a nonzero rational number and an irrational number irrational?

Yes, always.


Example of two irrational numbers the product of which is an irrational number?

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


What is the product of one irrational number and one rational number?

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


Is the product of any rational number and an irrational always irrational?

Yes.


Is the product of a nonzero rational and a irrational number irrational?

Yes, always.


Are numbers below 0.833 always irrational numbers?

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


Is the product of a rational number and irrational number always rational?

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


Does an irrational number times an irrational number equal an irrational number?

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


Is the product of two irrational numbers always an irrational number?

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.


What does a rational number times an irrational number equal?

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


Does there exist an irrational number such that its square root is rational?

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.).


Is the product of a rational and irrational number always irrational?

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


Why the product of nonzero rational number and a rational number is an 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)


Is it always sometimes or never true that the product of a non zero rational number and an irrational number is irrational?

It is always true.


Is a whole number always never or sometimes an irrational number?

Whole numbers can never be irrational.


Is an irrational number times an irrational number always irrational?

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


Is there any number x such that xยฒ is an irrational number and x's is a rational number?

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.