97 is a rational number.
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10.01 is a rational number
The square root of 97 is an irrational number. This is because the square root of 97 cannot be expressed as a fraction of two integers. In other words, the decimal representation of the square root of 97 goes on forever without repeating, making it an irrational number.
Rational
Such a product is always irrational - unless the rational number happens to be zero.
The sum of a rational and irrational number must be an irrational number.