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 \\(\frac{\sqrt4{y^3}}{\sqrt{y}}\\) as a single radical? explain.

Explanation:

Answer:

No. Use rational exponents: \(\frac{\sqrt[4]{y^{2}}}{\sqrt{y}}=\frac{y^{\frac{2}{4}}}{y^{\frac{1}{2}}}=y^{\frac{2}{4}-\frac{1}{2}} = y^{0}=1=\sqrt[4]{1}\) (or any index).