Basic Math Examples

${(\sqrt{8})}^{2} + b^{2} = c^{2}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $8$ as $2^{2} \cdot 2$ .

Tap for more steps...

Step 1.1.1

Factor $4$ out of $8$ .

${\sqrt{4 (2)}}^{2} + b^{2} = c^{2}$

Step 1.1.2

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

${\sqrt{2^{2} \cdot 2}}^{2} + b^{2} = c^{2}$

Step 1.2

Pull terms out from under the radical.

${(2 \sqrt{2})}^{2} + b^{2} = c^{2}$

Step 1.3

Apply the product rule to $2 \sqrt{2}$ .

$2^{2} {\sqrt{2}}^{2} + b^{2} = c^{2}$

Step 1.4

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

$4 {\sqrt{2}}^{2} + b^{2} = c^{2}$

Step 1.5

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

Tap for more steps...

Step 1.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$4 {(2^{\frac{1}{2}})}^{2} + b^{2} = c^{2}$

Step 1.5.2

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

$4 \cdot 2^{\frac{1}{2} \cdot 2} + b^{2} = c^{2}$

Step 1.5.3

Combine $\frac{1}{2}$ and $2$ .

$4 \cdot 2^{\frac{2}{2}} + b^{2} = c^{2}$

Step 1.5.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.5.4.1

Cancel the common factor.

$4 \cdot 2^{\frac{2}{2}} + b^{2} = c^{2}$

Step 1.5.4.2

Rewrite the expression.

$4 \cdot 2^{1} + b^{2} = c^{2}$

Step 1.5.5

Evaluate the exponent.

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

Step 1.6

Multiply $4$ by $2$ .

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

Step 2

Subtract $8$ from both sides of the equation.

$b^{2} = c^{2} - 8$

Step 3

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

$b = \pm \sqrt{c^{2} - 8}$

Step 4

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

Tap for more steps...

Step 4.1

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

$b = \sqrt{c^{2} - 8}$

Step 4.2

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

$b = - \sqrt{c^{2} - 8}$

Step 4.3

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

$b = \sqrt{c^{2} - 8}$

$b = - \sqrt{c^{2} - 8}$

$b = \sqrt{c^{2} - 8}$

$b = - \sqrt{c^{2} - 8}$