Final answer:
Expression (d) 2√x^2y^4 is in the simplest form because after simplification, all radicands are eliminated, making the square root disappear.
Step-by-step explanation:
The question asks which expression is in simplest form. Evaluating each option:
- (a) 2x^2√7y remains the same as it cannot be simplified further.
- (b) 2x^3√7y^4 can be simplified since y^4 under the square root is a perfect square, but without an actual expression, we cannot simplify further.
- (c) xy√16xy can be simplified since 16 is a perfect square, and √16 = 4. Therefore, the expression becomes 4xy^(3/2).
- (d) 2√x^2y^4 can be fully simplified since x^2 and y^4 are both perfect squares under the square root, yielding 2xy^2 after taking the square root of each term.
Comparing these options, (d) 2√x^2y^4 is in the simplest form, as radicands (numbers under the square root) have been simplified to eliminate the radical entirely.