Answer:
Part 5) Option b

Part 6) Option d.
![4y\sqrt[3]{2}\ mm](https://img.qammunity.org/2021/formulas/mathematics/middle-school/3saywbglveapt9dwvtei39hp1yjuf1zxe2.png)
Explanation:
Part 5) we know that
The area of a square is equal to

where
b is the length side of the square
we have

substitute

Solve for b
take square root both sides

Remember that

substitute

Applying property of exponents
![b=\sqrt{(2^2)(3)x^(2)}=[(2^2)(3)x^(2)]^{(1)/(2)}=[2^2x^2]^{(1)/(2)}3^{(1)/(2)}=2x√(3)\ ft](https://img.qammunity.org/2021/formulas/mathematics/middle-school/vba2v9f07wfluy5fkltoxyai0mlikkt0k6.png)
Part 6) we know that
The volume of a cube is equal to

where
b is the length side of the cube
we have

substitute

Solve for b
take cubic root both sides
![b=\sqrt[3]{128y^3}](https://img.qammunity.org/2021/formulas/mathematics/middle-school/tc8cdl6y5946n96rvmyaaj55zk97pnrm0s.png)
Remember that

substitute
![b=\sqrt[3]{(2^2)^3(2)y^3}](https://img.qammunity.org/2021/formulas/mathematics/middle-school/80eifj3anm7gq0wujy1m8oydnqxdn7go2r.png)
Applying property of exponents
![b=\sqrt[3]{(2^2)^3(2)y^3}=[(2^2)^3(2)y^3]^{(1)/(3)}=[(2^2)^3y^3]^{(1)/(3)}2^{(1)/(3)}=2^2y\sqrt[3]{2}=4y\sqrt[3]{2}\ mm](https://img.qammunity.org/2021/formulas/mathematics/middle-school/ulodvbeub403knd2ztkfoyelsf8w0nqd0q.png)