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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)

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โˆ™ 2016-12-15 15:04:14
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Q: Why the product of nonzero rational number and a rational number is an irrational?
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Related questions

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

It is always irrational.


What is product of a nonzero rational number and irrational number is?

It is irrational.


What is the product of a nonzero rational number and an irrational number?

The product will be irrational.


What is product of a nonzero rational number and a irrational number?

It is an irrational number.


The product of nonzero rational number and an irrational number is irrational?

Yes.


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

Yes, always.


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

Yes, always.


Can you multiply an irrational number by a rational number and the answer is rational?

The product of an irrational number and a rational number, both nonzero, is always irrational


Nonzero rational number and in irrational number makes what?

An irrational number.


Why the product of nonzero rational number and an irrational number is an irrational?

Suppose a is rational (and non-zero) and x is irrational. Suppose ax is rational;write ax = b where b is rational.Then x = b/a, and x would be rational, contradiction.


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 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.

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