Final answer:
The product of √(5x^8y^2), √(10x^3), and √(12y) simplifies to 10x^5y√6 using the properties of square roots and exponents.
Step-by-step explanation:
The student is asking for the product of square roots and this can be solved using rules of exponents and properties of square roots. To solve √(5x^8y^2) • √(10x^3) • √(12y), we can first multiply the radicals together because they share the same index (which is 2 for square roots). The product rule for radicals allows us to multiply under the same radical.
We get √(5 × 10 × 12 × x^8 × x^3 × y^2 × y), which simplifies to √(600x^{8+3}y^3). Following the exponent rules and simplifying further, we get √(600x^{11}y^3) = √(100 × 6x^{11}y^2 × y).
Since 100 is a perfect square we can take the square root of 100 and x^^11 evenly to get 10x^5√(6y^3) = 10x^5√(6y^2y) = 10x^5y√6 since y^2 is also a perfect square.
The final simplified form of the product is 10x^5y√6.