Complete the square.


Use de Moivre's theorem to compute the square roots of the right side.


Now, taking square roots on both sides, we have


Use de Moivre's theorem again to take square roots on both sides.



![\implies z = {w_2}^{1/2} = \boxed{\pm \sqrt[4]{3} \, \exp\left(-i\dfrac{5\pi}{12}\right)}](https://tex.z-dn.net/?f=%5Cimplies%20z%20%3D%20%7Bw_2%7D%5E%7B1%2F2%7D%20%3D%20%5Cboxed%7B%5Cpm%20%5Csqrt%5B4%5D%7B3%7D%20%5C%2C%20%5Cexp%5Cleft%28-i%5Cdfrac%7B5%5Cpi%7D%7B12%7D%5Cright%29%7D)
S
A
=
96
sq in.
Explanation:
V
=
s
3
64
=
s
3
find the cubic root of each side
3
√
64
=
s
4
=
s
so the side of the cube is 4 cu in.
The surface area of a cube is
S
A
=
n
A
where
S
A
is surface area,
n
is the number of faces, and
A
is the area of one face.
Te area of one face (
A
) is
s
2
so
A
=
16
n
=
6
S
A
=
6
⋅
16
=
96
When dividing indices with the same base, the rule is to subtract the index of the denominator from the index of the numerator, and to keep the base the same.
In this case, the index of our denominator is 6, and the index of the numerator is 2.
2-6 = -4
The answer is
.
Remember
(ab)/c=a(b/c)
and
b/b=1 when b=b
1.
8+9t+4=
8+4+9t=
12+9t=
9t+12
2. (56ab)/b=56a(b/b)=56a(1)=56a
3. divising negatives yeilds positive
-46/-2=46/2=23
1 6
--- = ---
a 18
- simplify 6/18, which should be 1/3. therefore, a = 3.