Question

The quotient property of radicals requires the indices of the radicals to be the same. Does this mean that it is not possible to write the 4th radicand of y cubed divided by the square root of y as a single radical? Explain

Answer 1

It is possible. Here's how:

`\sqrt[4]{ {y}^(3) } = {y}^{ (3)/(4) }`

`√(y) = {y}^{ (1)/(2) }`

`\frac{ \sqrt[4]{ {y}^(3) } }{ √(y) } = \frac{ {y}^{ (3)/(4) } }{ {y}^{ (1)/(2) } } = {y}^{ (1)/(4) } = \sqrt[4]{y}`