Final answer:
To simplify √-252 within the complex number system, we first break down the number into its prime factors. Then, we take the square root of the positive factors, resulting in the simplified expression 6√7i.
Step-by-step explanation:
In the complex number system, the square root of a negative number is called an imaginary number. To simplify √-252, we need to find the square root of -252. We can write -252 as -1 * 252. Breaking it down further, we have -1 * 2 * 2 * 3^2 * 7.
Now we can simplify the expression by taking the square root of the positive factors. The square root of 2 * 2 * 3^2 * 7 is 2 * 3 * √7, which gives us √(-252) = 6√7i.
Therefore, √-252 simplifies to 6√7i in the complex number system.
Learn more about Simplifying expressions within the complex number system