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Subjects>Math>Math & Arithmetic

Are the products of irrational numbers always irrational?

Anonymous

∙ 9y ago

Updated: 10/18/2022

No. The product of conjugate pairs is always rational.

So suppose sqrt(y) is the irrational square root of the rational number y. Then

Thus [x + sqrt(y)]*[x - sqrt(y)] = x^2 + x*sqrt(y) - x*sqrt(y) - sqrt(y)*sqrt(y)

= x^2 + y^2 which is rational.

Wiki User

∙ 9y ago

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Continue Learning about Math & Arithmetic

The sum of rational numbers and an irrational number?

It is always an irrational number.

Is the quotient of two irrational numbers is irrational?

In general, no. It is possible though. (2pi)/pi is rational. pi2/pi is irrational. The ratio of two rationals numbers is always rational and the ratio of a rational and an irrational is always irrational.

Are whole numbers rational or irrational?

Whole numbers are always rational

What is an irrational plus two rational numbers?

Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.

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

Whole numbers can never be irrational.

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