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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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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.
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 real number is always a rational number?
They are not. Sometimes they are irrational. Irrational numbers cannot be expressed as a fraction.
Is the product of three rational numbers rational or irrational?
A rational number in essence is any number that can be expressed as a fraction of integers (i.e. repeating decimal). Taking the product of any number of rational numbers will always yield another rational number.
Is the product of two rational numbers irrational?
The product of two rational numbers is always a rational number.
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 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 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.
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.
The sum of rational numbers and an irrational number?
It is always an irrational number.
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.
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.
