(C) First,calculate the square root of $289$.We know that $17 \times 17 = 289$,so $\sqrt{289} = 17$.Now,substitute this value into the expression: $\s

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(C) First,calculate the square root of $289$.We know that $17 \times 17 = 289$,so $\sqrt{289} = 17$.Now,substitute this value into the expression: $\sqrt{289} + 1 = 17 + 1 = 18$.Since $18$ is a whole number,it belongs to the set of integers.Therefore,$\sqrt{289} + 1$ is an integer.