Finite Math Examples

$\frac{\frac{213}{224} - 0.94}{\sqrt{\frac{0.94 \cdot 0.06}{224}}}$

Step 1

Multiply $0.94$ by $0.06$ .

$\frac{\frac{213}{224} - 0.94}{\sqrt{\frac{0.0564}{224}}}$

Step 2

Simplify the numerator.

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Step 2.1

To write $- 0.94$ as a fraction with a common denominator, multiply by $\frac{224}{224}$ .

$\frac{\frac{213}{224} - 0.94 \cdot \frac{224}{224}}{\sqrt{\frac{0.0564}{224}}}$

Step 2.2

Combine $- 0.94$ and $\frac{224}{224}$ .

$\frac{\frac{213}{224} + \frac{- 0.94 \cdot 224}{224}}{\sqrt{\frac{0.0564}{224}}}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{\frac{213 - 0.94 \cdot 224}{224}}{\sqrt{\frac{0.0564}{224}}}$

Step 2.4

Rewrite $\frac{213 - 0.94 \cdot 224}{224}$ in a factored form.

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Step 2.4.1

Multiply $- 0.94$ by $224$ .

$\frac{\frac{213 - 210.56}{224}}{\sqrt{\frac{0.0564}{224}}}$

Step 2.4.2

Subtract $210.56$ from $213$ .

$\frac{\frac{2.44}{224}}{\sqrt{\frac{0.0564}{224}}}$

Step 2.4.3

Divide $2.44$ by $224$ .

$\frac{0.01089285}{\sqrt{\frac{0.0564}{224}}}$

Step 3

Divide $0.0564$ by $224$ .

$\frac{0.01089285}{\sqrt{0.00025178}}$

Step 4

Multiply $\frac{0.01089285}{\sqrt{0.00025178}}$ by $\frac{\sqrt{0.00025178}}{\sqrt{0.00025178}}$ .

$\frac{0.01089285}{\sqrt{0.00025178}} \cdot \frac{\sqrt{0.00025178}}{\sqrt{0.00025178}}$

Step 5

Combine and simplify the denominator.

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Step 5.1

Multiply $\frac{0.01089285}{\sqrt{0.00025178}}$ by $\frac{\sqrt{0.00025178}}{\sqrt{0.00025178}}$ .

$\frac{0.01089285 \sqrt{0.00025178}}{\sqrt{0.00025178} \sqrt{0.00025178}}$

Step 5.2

Raise $\sqrt{0.00025178}$ to the power of $1$ .

$\frac{0.01089285 \sqrt{0.00025178}}{{\sqrt{0.00025178}}^{1} \sqrt{0.00025178}}$

Step 5.3

Raise $\sqrt{0.00025178}$ to the power of $1$ .

$\frac{0.01089285 \sqrt{0.00025178}}{{\sqrt{0.00025178}}^{1} {\sqrt{0.00025178}}^{1}}$

Step 5.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{0.01089285 \sqrt{0.00025178}}{{\sqrt{0.00025178}}^{1 + 1}}$

Step 5.5

Add $1$ and $1$ .

$\frac{0.01089285 \sqrt{0.00025178}}{{\sqrt{0.00025178}}^{2}}$

Step 5.6

Rewrite ${\sqrt{0.00025178}}^{2}$ as $0.00025178$ .

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Step 5.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{0.00025178}$ as ${0.00025178}^{\frac{1}{2}}$ .

$\frac{0.01089285 \sqrt{0.00025178}}{{({0.00025178}^{\frac{1}{2}})}^{2}}$

Step 5.6.2

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

$\frac{0.01089285 \sqrt{0.00025178}}{{0.00025178}^{\frac{1}{2} \cdot 2}}$

Step 5.6.3

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

$\frac{0.01089285 \sqrt{0.00025178}}{{0.00025178}^{\frac{2}{2}}}$

Step 5.6.4

Cancel the common factor of $2$ .

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Step 5.6.4.1

Cancel the common factor.

$\frac{0.01089285 \sqrt{0.00025178}}{{0.00025178}^{\frac{2}{2}}}$

Step 5.6.4.2

Rewrite the expression.

$\frac{0.01089285 \sqrt{0.00025178}}{{0.00025178}^{1}}$

Step 5.6.5

Evaluate the exponent.

$\frac{0.01089285 \sqrt{0.00025178}}{0.00025178}$

Step 6

Multiply $0.01089285$ by $\sqrt{0.00025178}$ .

$\frac{0.00017284}{0.00025178}$

Step 7

Divide $0.00017284$ by $0.00025178$ .

$0.68647743$