Basic Math Examples

$\sqrt{s^{2}} = \sqrt{114}$

Step 1

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{s^{2}}}^{2} = {\sqrt{114}}^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

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

${(s^{\frac{2}{2}})}^{2} = {\sqrt{114}}^{2}$

Step 2.2

Divide $2$ by $2$ .

${(s^{1})}^{2} = {\sqrt{114}}^{2}$

Step 2.3

Simplify the left side.

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Step 2.3.1

Multiply the exponents in ${(s^{1})}^{2}$ .

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Step 2.3.1.1

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

$s^{1 \cdot 2} = {\sqrt{114}}^{2}$

Step 2.3.1.2

Multiply $2$ by $1$ .

$s^{2} = {\sqrt{114}}^{2}$

Step 2.4

Simplify the right side.

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Step 2.4.1

Rewrite ${\sqrt{114}}^{2}$ as $114$ .

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Step 2.4.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{114}$ as $114^{\frac{1}{2}}$ .

$s^{2} = {(114^{\frac{1}{2}})}^{2}$

Step 2.4.1.2

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

$s^{2} = 114^{\frac{1}{2} \cdot 2}$

Step 2.4.1.3

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

$s^{2} = 114^{\frac{2}{2}}$

Step 2.4.1.4

Cancel the common factor of $2$ .

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Step 2.4.1.4.1

Cancel the common factor.

$s^{2} = 114^{\frac{2}{2}}$

Step 2.4.1.4.2

Rewrite the expression.

$s^{2} = 114^{1}$

Step 2.4.1.5

Evaluate the exponent.

$s^{2} = 114$

Step 3

Solve for $s$ .

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Step 3.1

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

$s = \pm \sqrt{114}$

Step 3.2

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

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Step 3.2.1

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

$s = \sqrt{114}$

Step 3.2.2

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

$s = - \sqrt{114}$

Step 3.2.3

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

$s = \sqrt{114}, - \sqrt{114}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$s = \sqrt{114}, - \sqrt{114}$

Decimal Form:

$s = 10.67707825 \dots, - 10.67707825 \dots$