Final answer:
The negative square root of 17 is not a rational number because it cannot be expressed as a quotient of two integers. Therefore, the statement is False.
Step-by-step explanation:
The question asks to determine the nature of the negative square root of 17. A rational number can be expressed as the quotient of two integers, where the denominator is not zero. The negative square root of any positive non-square integer, such as 17, is an irrational number. Since it cannot be expressed as a quotient of two integers, the negative square root of 17 is not a rational number. A rational number is a number that can be expressed as a fraction of two integers. The negative square root of 17, denoted as -sqrt(17), is an irrational number because it cannot be expressed as a fraction. It is a non-repeating, non-terminating decimal.
Therefore, the statement 'The negative square root of 17 is a rational number' is False.