The square root of 17 is not a rational number. A rational number is defined as any number that can be expressed as the quotient or fraction a/b of two integers, where a is the numerator and b is the denominator, and b is not zero.
To determine whether the square root of 17 is rational, let’s consider its value. The square root of 17 is approximately 4.1231. This number cannot be expressed as a simple fraction of two integers, meaning it cannot be accurately represented as a/b without resulting in a non-repeating, non-terminating decimal.
Moreover, 17 is not a perfect square, which means that its square root cannot be simplified into a whole number or a simple fraction. Since it does not fulfill the criteria for being a rational number, we conclude that the square root of 17 is an irrational number.