Simplify (0.2167-0.25)/(( square root of (0.25)(0.75))/420)

$\frac{0.2167 - 0.25}{\frac{\sqrt{(0.25) (0.75)}}{420}}$

Multiply the numerator by the reciprocal of the denominator.

$(0.2167 - 0.25) \frac{420}{\sqrt{(0.25) (0.75)}}$

Multiply $0.25$ by $0.75$ .

$(0.2167 - 0.25) \frac{420}{\sqrt{0.1875}}$

Subtract $0.25$ from $0.2167$ .

$- 0.0333 \frac{420}{\sqrt{0.1875}}$

Multiply $\frac{420}{\sqrt{0.1875}}$ by $\frac{\sqrt{0.1875}}{\sqrt{0.1875}}$ .

$- 0.0333 (\frac{420}{\sqrt{0.1875}} \cdot \frac{\sqrt{0.1875}}{\sqrt{0.1875}})$

Combine and simplify the denominator.

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Multiply $\frac{420}{\sqrt{0.1875}}$ and $\frac{\sqrt{0.1875}}{\sqrt{0.1875}}$ .

$- 0.0333 \frac{420 \sqrt{0.1875}}{\sqrt{0.1875} \sqrt{0.1875}}$

Raise $\sqrt{0.1875}$ to the power of $1$ .

$- 0.0333 \frac{420 \sqrt{0.1875}}{{\sqrt{0.1875}}^{1} \sqrt{0.1875}}$

Raise $\sqrt{0.1875}$ to the power of $1$ .

$- 0.0333 \frac{420 \sqrt{0.1875}}{{\sqrt{0.1875}}^{1} {\sqrt{0.1875}}^{1}}$

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

$- 0.0333 \frac{420 \sqrt{0.1875}}{{\sqrt{0.1875}}^{1 + 1}}$

Add $1$ and $1$ .

$- 0.0333 \frac{420 \sqrt{0.1875}}{{\sqrt{0.1875}}^{2}}$

Rewrite ${\sqrt{0.1875}}^{2}$ as $0.1875$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{0.1875}$ as ${0.1875}^{\frac{1}{2}}$ .

$- 0.0333 \frac{420 \sqrt{0.1875}}{{({0.1875}^{\frac{1}{2}})}^{2}}$

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

$- 0.0333 \frac{420 \sqrt{0.1875}}{{0.1875}^{\frac{1}{2} \cdot 2}}$

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

$- 0.0333 \frac{420 \sqrt{0.1875}}{{0.1875}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$- 0.0333 \frac{420 \sqrt{0.1875}}{{0.1875}^{\frac{2}{2}}}$

Divide $1$ by $1$ .

$- 0.0333 \frac{420 \sqrt{0.1875}}{{0.1875}^{1}}$

Evaluate the exponent.

$- 0.0333 \frac{420 \sqrt{0.1875}}{0.1875}$

Evaluate the root.

$- 0.0333 \frac{420 \cdot 0.4330127}{0.1875}$

Multiply $420$ by $0.4330127$ .

$- 0.0333 (\frac{181.86533479}{0.1875})$

Divide $181.86533479$ by $0.1875$ .

$- 0.0333 \cdot 969.94845223$

Multiply $- 0.0333$ by $969.94845223$ .

$- 32.29928345$

Simplify (0.2167-0.25)/(( square root of (0.25)(0.75))/420)

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