r^8=16

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Solution for r^8=16 equation: 


Simplifying
r8 = 16

Solving
r8 = 16

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Simplifying
r8 = 16

Reorder the terms:
-16 + r8 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + r8 = 0

Factor a difference between two squares.
(4 + r4)(-4 + r4) = 0

Factor a difference between two squares.
(4 + r4)((2 + r2)(-2 + r2)) = 0


Subproblem 1
Set the factor '(4 + r4)' equal to zero and attempt to solve:

Simplifying
4 + r4 = 0

Solving
4 + r4 = 0

Move all terms containing r to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + r4 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + r4 = 0 + -4
r4 = 0 + -4

Combine like terms: 0 + -4 = -4
r4 = -4

Simplifying
r4 = -4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(2 + r2)' equal to zero and attempt to solve:

Simplifying
2 + r2 = 0

Solving
2 + r2 = 0

Move all terms containing r to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + r2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + r2 = 0 + -2
r2 = 0 + -2

Combine like terms: 0 + -2 = -2
r2 = -2

Simplifying
r2 = -2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(-2 + r2)' equal to zero and attempt to solve:

Simplifying
-2 + r2 = 0

Solving
-2 + r2 = 0

Move all terms containing r to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + r2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + r2 = 0 + 2
r2 = 0 + 2

Combine like terms: 0 + 2 = 2
r2 = 2

Simplifying
r2 = 2

Take the square root of each side:
r = {-1.414213562, 1.414213562}
Solution
r = {-1.414213562, 1.414213562}

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