Basic Math Examples

$\frac{5 \sqrt{S}}{2 \sqrt{S} + \sqrt{4}}$

Step 1

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

$\frac{5 \sqrt{S}}{2 S^{\frac{1}{2}} + \sqrt{4}}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4}$ as $4^{\frac{1}{2}}$ .

$\frac{5 \sqrt{S}}{2 S^{\frac{1}{2}} + 4^{\frac{1}{2}}}$

Step 3

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

$\frac{5 \sqrt{S}}{2 S^{\frac{1}{2}} + {(2^{2})}^{\frac{1}{2}}}$

Step 4

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

$\frac{5 \sqrt{S}}{2 S^{\frac{1}{2}} + 2^{2 (\frac{1}{2})}}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Cancel the common factor.

$\frac{5 \sqrt{S}}{2 S^{\frac{1}{2}} + 2^{2 (\frac{1}{2})}}$

Step 5.2

Rewrite the expression.

$\frac{5 \sqrt{S}}{2 S^{\frac{1}{2}} + 2^{1}}$

Step 6

Evaluate the exponent.

$\frac{5 \sqrt{S}}{2 S^{\frac{1}{2}} + 2}$

Step 7

Factor $2$ out of $2 S^{\frac{1}{2}} + 2$ .

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Step 7.1

Factor $2$ out of $2 S^{\frac{1}{2}}$ .

$\frac{5 \sqrt{S}}{2 (S^{\frac{1}{2}}) + 2}$

Step 7.2

Factor $2$ out of $2$ .

$\frac{5 \sqrt{S}}{2 (S^{\frac{1}{2}}) + 2 (1)}$

Step 7.3

Factor $2$ out of $2 (S^{\frac{1}{2}}) + 2 (1)$ .

$\frac{5 \sqrt{S}}{2 (S^{\frac{1}{2}} + 1)}$