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 root of y^3)/(square root of y)) as a single radical? Explain.

Answer 1

Answer:

$\sqrt[4]{y}$

Step-by-step explanation:

The quotient property of radicals requires the indices of the radicals to be the same.

This statement is true and is applicable also for expressing the ((4th root of y^3)/(square root of y)) as a single radical.

The given expression is  

$\frac{\sqrt[4]{y^{3}}}{\sqrt{y} }$

Now, $\sqrt{y}$ can also be written as $\sqrt[4]{y^{2}}$, and hence,

$\frac{\sqrt[4]{y^{3}}}{\sqrt{y} }$

= $\frac{\sqrt[4]{y^{3}}}{\sqrt[4]{y^{2}}}$

= $\sqrt[4]{\frac{y^{3}}{y^{2}}}$

= $\sqrt[4]{y}$ (Answer)

Answer 2

Answer:

The radicals are the power of the same base so they can be written using rational exponents. Simplified the quotient of the exponential expression by getting a common denominator and subtracting exponents. The simplified expression is the 4th root of y

Step-by-step explanation:

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