Basic Math Examples

$20^{2} = {(2 \cdot \sqrt{S})}^{2}$

Step 1

Simplify ${(2 \cdot \sqrt{S})}^{2}$ .

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Step 1.1

Simplify the expression.

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Step 1.1.1

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

$20^{2} = 2^{2} {\sqrt{S}}^{2}$

Step 1.1.2

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

$20^{2} = 4 {\sqrt{S}}^{2}$

Step 1.2

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

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Step 1.2.1

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

$20^{2} = 4 {(S^{\frac{1}{2}})}^{2}$

Step 1.2.2

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

$20^{2} = 4 S^{\frac{1}{2} \cdot 2}$

Step 1.2.3

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

$20^{2} = 4 S^{\frac{2}{2}}$

Step 1.2.4

Cancel the common factor of $2$ .

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Step 1.2.4.1

Cancel the common factor.

$20^{2} = 4 S^{\frac{2}{2}}$

Step 1.2.4.2

Rewrite the expression.

$20^{2} = 4 S^{1}$

Step 1.2.5

Simplify.

$20^{2} = 4 S$

Step 2

Rewrite the equation as $4 S = 20^{2}$ .

$4 S = 20^{2}$

Step 3

Divide each term in $4 S = 20^{2}$ by $4$ and simplify.

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Step 3.1

Divide each term in $4 S = 20^{2}$ by $4$ .

$\frac{4 S}{4} = \frac{20^{2}}{4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{4 S}{4} = \frac{20^{2}}{4}$

Step 3.2.1.2

Divide $S$ by $1$ .

$S = \frac{20^{2}}{4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $20$ to the power of $2$ .

$S = \frac{400}{4}$

Step 3.3.2

Divide $400$ by $4$ .

$S = 100$