what is the square root of 64y^{16}?\n4y^{4}\n4y^{8}\n8y^{4}\n8y^{8}

Explanation:

Step1: Find square - root of 64

The square - root of 64 is $\sqrt{64}=8$ since $8\times8 = 64$.

Step2: Find square - root of $y^{16}$

Using the rule $\sqrt{x^n}=x^{\frac{n}{2}}$, for $x = y$ and $n = 16$, we have $\sqrt{y^{16}}=y^{\frac{16}{2}}=y^8$.

Step3: Combine the results

The square - root of $64y^{16}$ is $\sqrt{64y^{16}}=\sqrt{64}\times\sqrt{y^{16}} = 8y^8$.

Answer:

D. $8y^8$