Basic Math Examples

$\sqrt{s^{2}} = \sqrt{784}$

Step 1

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

${\sqrt{s^{2}}}^{2} = {\sqrt{784}}^{2}$

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 $s^{\frac{2}{2}}$ .

${(s^{\frac{2}{2}})}^{2} = {\sqrt{784}}^{2}$

Step 2.2

Divide $2$ by $2$ .

${(s^{1})}^{2} = {\sqrt{784}}^{2}$

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, ${(a^{m})}^{n} = a^{m n}$ .

$s^{1 \cdot 2} = {\sqrt{784}}^{2}$

Step 2.3.1.2

Multiply $2$ by $1$ .

$s^{2} = {\sqrt{784}}^{2}$

Step 2.4

Simplify the right side.

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Step 2.4.1

Simplify ${\sqrt{784}}^{2}$ .

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Step 2.4.1.1

Rewrite $784$ as $28^{2}$ .

$s^{2} = {\sqrt{28^{2}}}^{2}$

Step 2.4.1.2

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

$s^{2} = 28^{2}$

Step 2.4.1.3

Raise $28$ to the power of $2$ .

$s^{2} = 784$

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.

$s = \pm \sqrt{784}$

Step 3.2

Simplify $\pm \sqrt{784}$ .

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Step 3.2.1

Rewrite $784$ as $28^{2}$ .

$s = \pm \sqrt{28^{2}}$

Step 3.2.2

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

$s = \pm 28$

Step 3.3

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

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Step 3.3.1

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

$s = 28$

Step 3.3.2

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

$s = - 28$

Step 3.3.3

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

$s = 28, - 28$