Which of these expressions is in simplified form?

A. a ^3 sqrt 4 - b ^3 sqrt 2 / 2
B. sqrt 1/2x + sqrt 1/2z
C. x^2 - 3x sqrt y / sqrt 3
D. sqrt 125x - x^2

It is hard to understand what you mean without parentheses but the way I see it A can be simplified since sqrt 4 = 2 and C can be written as x^2-sqrt (3yx^2). So B and D are simplified.

To determine which expression is in simplified form, we need to look for any opportunities to simplify or combine like terms, rationalize the denominator, and simplify any radicals.

Let's evaluate each option:

A. a^3 sqrt 4 - b^3 sqrt 2 / 2
To simplify, we need to evaluate the square root of 4, which is 2. This gives us:
a^3 * 2 - b^3 sqrt 2 / 2

B. sqrt 1/2x + sqrt 1/2z
There are two square roots to evaluate. The square root of 1/2 is (√1)/(√2) = 1/√2, so the expression becomes:
1/√2x + 1/√2z

C. x^2 - 3x sqrt y / sqrt 3
This expression already appears to be simplified, as there are no like terms to combine or square roots to rationalize.

D. sqrt 125x - x^2
The square root of 125 can be simplified to 5√5, resulting in:
5√5x - x^2

Based on this analysis, option C does not require any further simplification and therefore is the expression in simplified form.