Final answer:
The expression '-2 ± √104 over 4' simplifies to '-1 ± √26 over 2' by first simplifying √104 to 2√26 and then reducing the expression by dividing the numerator by the common factor of 2.
Step-by-step explanation:
The student has asked to simplify the following expression to its radical form:
-2 ± √104 over 4
To begin, we can simplify √104. The number 104 is not a perfect square, but it can be broken down into 4 × 26, where 4 is a perfect square. Taking the square root of 4 gives us 2, and we are left with 2√26. Therefore, √104 simplifies to 2√26. Now, we can rewrite the original expression as:
(-2 ± 2√26) / 4
Since we have a common factor of 2 in the numerator, we can divide each term by 2 to simplify further:
(-1 ± √26) / 2
Thus, the expression simplifies to -1 ± √26 over 2.