Simplify the radical. Assume that all variables represent positive real numbers. $\sqrt [ 3 ] { 96 y ^ { 23 } }$
A) $2 y \sqrt [ 3 ] { 12 y ^ { 20 } }$
B) $2 y ^ { 7 } \sqrt [ 3 ] { 12 y ^ { 2 } }$
C) $8 y ^ { 21 } \sqrt [ 3 ] { 12 y ^ { 2 } }$
D) $y ^ { 7 } \sqrt [ 3 ] { 96 y ^ { 2 } }$

Question

Quizplus · Accepted Answer

First, factor 96 into $2^5 \times 3$. For $y^{23}$, separate it into $y^{21} \times y^2$ to make the exponent divisible by 3. This gives $2^5 y^{21} \times 3y^2$. Taking the cube root of $2^5 y^{21}$ gives $2y^7$ because $2^5$ can be simplified to $2^3 \times 2^2$, and $y^{21}$ is divisible by 3. The remaining part under the cube root is $12y^2$. Therefore, the simplified form is $2y^7 \sqrt[3]{12y^2}$.

Simplify the Radical 96y233\sqrt [ 3 ] { 96 y ^ { 23 } }396y23​

Simplify the Radical $\sqrt [ 3 ] { 96 y ^ { 23 } }$