Final answer:
After simplifying the square root of each factor in sqrt(8x^7y^8), we find that none of the provided answer choices exactly match the simplified expression, suggesting an issue in the question or answer choices.
Step-by-step explanation:
To find an expression equivalent to sqrt(8x^7y^8), we can simplify the square root of a product by taking the square root of each factor separately.
The square root of 8 is 2*sqrt(2) because 8 is 4*2 and 4 is a perfect square. sqrt(x^7) can be broken down into x^3*sqrt(x) because x^6 is a perfect square. With sqrt(y^8), since y^8 is a perfect square (y^4*y^4), the square root is simply y^4.
Combining these we have 2*sqrt(2)*x^3*sqrt(x)*y^4. Since there's no further simplification, none of the answer choices (A) 4x^3y^4, (B) 2x^3y^4, (C) 2x^4y^4, or (D) 4x^4y^4 exactly matches our expression, which implies there's a potential error in the question or answer choices.