Write 5 square root y^3 3 square root y^11 as a single radical using the smallest possible root
To simplify the expression, let's break down each term and rewrite it using the smallest possible root.
1. Square root of y^3 can be written as y^(3/2) since y^(3/2) means taking the square root of y^3.
2. Similarly, the square root of y^11 can be written as y^(11/2).
Now, let's multiply both terms:
5 square root y^3 * 3 square root y^11 = 5 * 3 * y^(3/2) * y^(11/2)
The coefficient 5 and 3 can be multiplied together to get 15, and we can simplify the power of y by adding the exponents:
15 * y^(3/2 + 11/2) = 15 * y^(14/2) = 15 * y^7
Therefore, 5 square root y^3 * 3 square root y^11 can be simplified as 15y^7.