Whenever you're completing operations on real numbers, we need to keep in mind several Real Number Properties:

Property 9: If the product of two numbers is negative, exactly one of the two numbers is negative.
Property 10: The absolute value of the sum of two integers is always less than or equal to the sum of the absolute values of the two integers. That is, $$|a + b| \leq |a| + |b|$$
Property 11: The absolute value of the product of two integers is equal to the product of the absolute values of the two integers. That is, $$|ab| = |a||b|$$
Property 12: If $a = 1$, $$a = a^2 = \sqrt{a}$$ while if $a > 1$, $$a^2 > a > \sqrt{a}$$ and if $0< a < 1$, $$\sqrt{a} > a > a^2$$