Final answer:
The solution to the negative square root of 75, to the nearest integer, is -9. This is obtained by first determining the square root of 75, approximately 8.66, then taking the negative of that value, and rounding to the nearest integer.
Step-by-step explanation:
The student is asking for the nearest integer to the negative square root of 75. To find the square root of 75, we can simplify it by recognizing that 75 equals 25 times 3. Thus, the square root of 75 can be expressed as the square root of 25 times the square root of 3, which is 5 times the square root of 3. The approximate decimal value for the square root of 3 is 1.732, so the square root of 75 is approximately 5 times 1.732, which gives us roughly 8.66.
Since we need the negative square root, we take the negative of that result, which is approximately -8.66. To round to the nearest integer, we look at the decimal part, and since it is greater than .5, we round down to -9 as the negative square root is always less than zero.
Therefore, the solution to the negative square root of 75 rounded to the nearest integer is -9.