Final answer:
The expression -3√25xy^5 simplifies to -15xy^2√y, by simplifying the square root of 25 to 5 and separating y^5 into y^4 and y to get y^2√y. The final answer is -15xy^2√y.
Step-by-step explanation:
To simplify the expression -3√25xy^5, we need to simplify the square root and then multiply by -3.
First, let's simplify √25xy^5. The square root of 25 is 5, and we can simplify √y^5 as y^2√y because y^5 = y^4×y and we know that y^4 is a perfect square since it can be written as (y^2)^2. However, the square root of x and y cannot be simplified further as they are not perfect squares or do not have an exponent that is a multiple of 2. So we rewrite the square root as 5xy^2√y.
Now we multiply this by -3:
-3 × (5xy^2√y) = -15xy^2√y.
We keep the square root √y as it cannot be simplified further. Thus, the simplified form of -3√25xy^5 is -15xy^2√y which corresponds to choice (a) -15√xy^5.