Simplify.
\[
\sqrt{24 y^{8}}
\]

Assume that the variable $y$ represents a positive real number.
$\square$
\[
\sqrt{\square} \quad \square
\]

Answer

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Answer

Final Answer: The simplified form of the given expression is $\boxed{2\sqrt{6}y^{4}}$.

Steps

Step 1 ：The given expression is $\sqrt{24 y^{8}}$.

Step 2 ：24 can be factored into 4 and 6, where 4 is a perfect square.

Step 3 ：$y^{8}$ can be written as $(y^{4})^{2}$, which is also a perfect square.

Step 4 ：So, we can simplify the expression by taking the square root of these perfect squares.

Step 5 ：The simplified expression is $2\sqrt{6}y^{4}$.

Step 6 ：Final Answer: The simplified form of the given expression is $\boxed{2\sqrt{6}y^{4}}$.