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If the product of two irrationals is a rational, then they are both the same radical of a non-perfect square. For example, radical 5 times radical 5 is 5, since that is by definiton what a radical is.

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Q: When the product of two irrational numbers equals a rational number what are the two factors called?
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Related questions

What product is true about the irrational and rational numbers?

The product of 2 rationals must be rational. The product of a rational and an irrational is irrational (unless the rational is 0) The product of two irrationals can be either rational or irrational.


When the product of two irrational numbers equals a rational number then what are the factors called?

They are called conjugates.


What happens when two irrational numbers are multiplied?

You get a product which can be rational or irrational.


Is the product of two rational numbers irrational?

The product of two rational numbers is always a rational number.


Why is the product of two rational number irrational?

The question is nonsense because the product of two rational numbers is never irrational.


When the product of two irrational or imaginary numbers equals a rational number then the two factors are called?

They are called conjugates.


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.


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 there any number x such that x² 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.


Is the product of any two irrational numbers is an irrational?

No. The product of sqrt(2) and sqrt(2) is 2, a rational number. Consider surds of the form a+sqrt(b) where a and b are rational but sqrt(b) is irrational. The surd has a conjugate pair which is a - sqrt(b). Both these are irrational, but their product is a2 - b, which is rational.


Why is the product of a non - zero rational number and an irrational number is irrational?

Let q be a non-zero rational and x be an irrational number.Suppose q*x = p where p is rational. Then x = p/q. Then, since the set of rational numbers is closed under division (by non-zero numbers), p/q is rational. But that means that x is rational, which contradicts x being irrational. Therefore the supposition that q*x is rational must be false ie the product of a non-zero rational and an irrational cannot be rational.