Solve for c 10^2+10^2=c^2

$10^{2} + 10^{2} = c^{2}$

Step 1

Rewrite the equation as $c^{2} = 10^{2} + 10^{2}$ .

$c^{2} = 10^{2} + 10^{2}$

Step 2

Add $10^{2}$ and $10^{2}$ .

$c^{2} = 2 \cdot 10^{2}$

Step 3

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$c = \pm \sqrt{2 \cdot 10^{2}}$

Step 4

Simplify $\pm \sqrt{2 \cdot 10^{2}}$ .

Rewrite $\sqrt{2 \cdot 10^{2}}$ as $\sqrt{2} \cdot \sqrt{10^{2}}$ .

$c = \pm \sqrt{2} \cdot \sqrt{10^{2}}$

Evaluate the root.

$c = \pm 1.41421356 \cdot \sqrt{10^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$c = \pm 1.41421356 \cdot 10$

Raise $10$ to the power of $1$ .

$c = \pm 1.41421356 \cdot 10^{1}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$c = 1.41421356 \cdot 10^{1}$

Next, use the negative value of the $\pm$ to find the second solution.

$c = - 1.41421356 \cdot 10^{1}$

The complete solution is the result of both the positive and negative portions of the solution.

$c = 1.41421356 \cdot 10^{1}, - 1.41421356 \cdot 10^{1}$

Step 6

The result can be shown in multiple forms.

Scientific Notation:

$c = 1.41421356 \cdot 10^{1}, - 1.41421356 \cdot 10^{1}$

Expanded Form:

$c = 14.14213562, - 14.14213562$