Algebra Examples

$4^{2} + 4^{2} = c^{2}$

Step 1

Rewrite the equation as $c^{2} = 4^{2} + 4^{2}$ .

$c^{2} = 4^{2} + 4^{2}$

Step 2

Add $4^{2}$ and $4^{2}$ .

$c^{2} = 2 \cdot 4^{2}$

Step 3

Rewrite $4$ as $2^{2}$ .

$c^{2} = 2 \cdot {(2^{2})}^{2}$

Step 4

Multiply the exponents in ${(2^{2})}^{2}$ .

Tap for more steps...

Step 4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 4.2

Multiply $2$ by $2$ .

$c^{2} = 2 \cdot 2^{4}$

Step 5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$c^{2} = 2^{1 + 4}$

Step 6

Add $1$ and $4$ .

$c^{2} = 2^{5}$

Step 7

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

$c = \pm \sqrt{2^{5}}$

Step 8

Simplify $\pm \sqrt{2^{5}}$ .

Tap for more steps...

Step 8.1

Raise $2$ to the power of $5$ .

$c = \pm \sqrt{32}$

Step 8.2

Rewrite $32$ as $4^{2} \cdot 2$ .

Tap for more steps...

Step 8.2.1

Factor $16$ out of $32$ .

$c = \pm \sqrt{16 (2)}$

Step 8.2.2

Rewrite $16$ as $4^{2}$ .

$c = \pm \sqrt{4^{2} \cdot 2}$

Step 8.3

Pull terms out from under the radical.

$c = \pm 4 \sqrt{2}$

Step 9

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

Tap for more steps...

Step 9.1

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

$c = 4 \sqrt{2}$

Step 9.2

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

$c = - 4 \sqrt{2}$

Step 9.3

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

$c = 4 \sqrt{2}, - 4 \sqrt{2}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$c = 4 \sqrt{2}, - 4 \sqrt{2}$

Decimal Form:

$c = 5.65685424 \dots, - 5.65685424 \dots$