Basic Math Examples

$2 s^{2} = 4 \sqrt{2}$

Step 1

Divide each term in $2 s^{2} = 4 \sqrt{2}$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 s^{2} = 4 \sqrt{2}$ by $2$ .

$\frac{2 s^{2}}{2} = \frac{4 \sqrt{2}}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 s^{2}}{2} = \frac{4 \sqrt{2}}{2}$

Step 1.2.1.2

Divide $s^{2}$ by $1$ .

$s^{2} = \frac{4 \sqrt{2}}{2}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Cancel the common factor of $4$ and $2$ .

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Step 1.3.1.1

Factor $2$ out of $4 \sqrt{2}$ .

$s^{2} = \frac{2 (2 \sqrt{2})}{2}$

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Factor $2$ out of $2$ .

$s^{2} = \frac{2 (2 \sqrt{2})}{2 (1)}$

Step 1.3.1.2.2

Cancel the common factor.

$s^{2} = \frac{2 (2 \sqrt{2})}{2 \cdot 1}$

Step 1.3.1.2.3

Rewrite the expression.

$s^{2} = \frac{2 \sqrt{2}}{1}$

Step 1.3.1.2.4

Divide $2 \sqrt{2}$ by $1$ .

$s^{2} = 2 \sqrt{2}$

Step 2

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

$s = \pm \sqrt{2 \sqrt{2}}$

Step 3

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

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Step 3.1

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

$s = \sqrt{2 \sqrt{2}}$

Step 3.2

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

$s = - \sqrt{2 \sqrt{2}}$

Step 3.3

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

$s = \sqrt{2 \sqrt{2}}, - \sqrt{2 \sqrt{2}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$s = \sqrt{2 \sqrt{2}}, - \sqrt{2 \sqrt{2}}$

Decimal Form:

$s = 1.68179283 \dots, - 1.68179283 \dots$