First, the answer here is wrong! You wrote the radical incorrectly.
The original problem is asking for the positive number whose square is [imath](1-\sqrt{13})^2[/imath]. You might at first think the answer is obviously [imath]1-\sqrt{13}[/imath]. But there are two numbers that have the same square (one positive and one negative); for example, both 3 and -3 have their square equal to 9, and the square root of 9 is the positive one, 3. In your case, the other number is [imath]\sqrt{13}-1[/imath].
You need to determine which of the two is positive, and it turns out to be the latter.
A better way to show the work, in my mind, would be to use the formula [imath]\sqrt{x^2}=|x|[/imath]. Can you see why this would be true regardless of whether x is positive or negative? So you'd write [imath]\sqrt{(1-\sqrt{13})^2} = |1-\sqrt{13}| = \sqrt{13}-1[/imath].