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Multiplying a rational number with an irrational number will equal a rational number

User Kworr
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No, multiplying an irrational number by a rational number always results in an irrational number, not a rational one.

In general, the product of an irrational number and a rational number is irrational, meaning that it cannot be expressed as a simple fraction of two integers.

An irrational number is defined as a number that cannot be represented as the quotient of two integers, and examples include the square root of 2 or the mathematical constant π.

When you multiply an irrational number by a rational number, the result typically retains the irrational nature of the original number.

The reasoning lies in the fact that multiplying an irrational number by any non-zero rational number does not eliminate the non-repeating, non-terminating decimals inherent in irrational numbers.

For instance, if you consider the irrational number √2 and multiply it by a rational number like 2/3, the result (√2) * (2/3) remains irrational.

The product is a combination of the irrationality of √2 and the rationality of 2/3, resulting in an irrational number.

Therefore, it is a fundamental mathematical property that the multiplication of an irrational number by a rational number typically yields an irrational result.

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

User Fernacolo
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