What is the solution to the square root of -75 to the nearest integer
To find the solution to the square root of -75 to the nearest integer, we need to first determine if the square root of a negative number is defined in the real number system.
In the real number system, the square root of a negative number is not a real number because any real number squared will always result in a non-negative value. However, it is defined in the complex number system.
The complex numbers are represented in the form a + bi, where "a" and "b" are real numbers, and "i" is the imaginary unit (√-1).
To find the square root of -75, we can express it as √(75 * -1).
Next, we simplify the expression:
√(75 * -1) = √75 * √-1
The square root of 75 is an irrational number since it is not a perfect square. So, we have:
√75 ≈ 8.66 (rounded to two decimal places)
Now, we need to find the square root of -1, which is the imaginary unit "i".
Therefore, the square root of -75 can be written as:
√-75 = 8.66i (to the nearest integer, which is the closest whole number, we round up to 9)
So, the solution to the square root of -75 to the nearest integer is 9.