what is the square root of $64y^{16}$?\n$4y^{4}$\n$4y^{8}$\n$8y^{4}$\n$8y^{8}$
what is the square root of $64y^{16}$?\n$4y^{4}$\n$4y^{8}$\n$8y^{4}$\n$8y^{8}$
Answer
Explanation:
Step1: Find square - root of coefficient
We know that $\sqrt{64}=8$ since $8\times8 = 64$.
Step2: Use exponent rule for square - root
For $y^{16}$, using the rule $\sqrt{a^m}=a^{\frac{m}{2}}$, we have $\sqrt{y^{16}}=y^{\frac{16}{2}} = y^8$.
Step3: Combine results
The square - root of $64y^{16}$ is the product of the square - root of the coefficient and the square - root of the variable part, so $\sqrt{64y^{16}}=8y^8$.
Answer:
D. $8y^8$