State true or false: Product of a rational and an irrational number is always irrational.

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True

False

answer is B.

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Detailed Solution

A statement says that the product of a rational number and an irrational number is a rational number, and we have to state if it’s true or not.
Now, we know that any operation, be it addition, subtraction, multiplication and division, performed between a rational number and an irrational number gives the result as an irrational number.
But, if we take the product of a rational number say 0 with an irrational number say

2

, the product will be

0 × 2 = 0

.
This contradicts the given statement as 0 is rational number.
Hence, the statement is false.
Product of a rational and an irrational number is only irrational when not multiplied by 0.
So, the correct option is 2.

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