Pre-Algebra Examples

6^{2} + 8^{2} = c^{2}

$6^{2} + 8^{2} = c^{2}$

Step 1

Rewrite the equation as

c^{2} = 6^{2} + 8^{2}

$c^{2} = 6^{2} + 8^{2}$ .

c^{2} = 6^{2} + 8^{2}

$c^{2} = 6^{2} + 8^{2}$

Step 2

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

c = \pm \sqrt{6^{2} + 8^{2}}

$c = \pm \sqrt{6^{2} + 8^{2}}$

Step 3

Simplify

\pm \sqrt{6^{2} + 8^{2}}

$\pm \sqrt{6^{2} + 8^{2}}$ .

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Step 3.1

Raise

6

$6$ to the power of

2

$2$ .

c = \pm \sqrt{36 + 8^{2}}

$c = \pm \sqrt{36 + 8^{2}}$

Step 3.2

Raise

8

$8$ to the power of

2

$2$ .

c = \pm \sqrt{36 + 64}

$c = \pm \sqrt{36 + 64}$

Step 3.3

Add

36

$36$ and

64

$64$ .

c = \pm \sqrt{100}

$c = \pm \sqrt{100}$

Step 3.4

Rewrite

100

$100$ as

10^{2}

$10^{2}$ .

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

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

Step 3.5

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

c = \pm 10

$c = \pm 10$

c = \pm 10

$c = \pm 10$

Step 4

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

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Step 4.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

c = 10

$c = 10$

Step 4.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

c = - 10

$c = - 10$

Step 4.3

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

c = 10, - 10

$c = 10, - 10$

c = 10, - 10

$c = 10, - 10$

6^{2} + 8^{2} = c^{2}

$6^{2} + 8^{2} = c^{2}$

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