Basic Math Examples

$R = \sqrt{\frac{Gm K}{F}}$

Step 1

Rewrite the equation as $\sqrt{\frac{Gm K}{F}} = R$ .

$\sqrt{\frac{Gm K}{F}} = R$

Step 2

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

${\sqrt{\frac{Gm K}{F}}}^{2} = R^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{Gm K}{F}}$ as ${(\frac{Gm K}{F})}^{\frac{1}{2}}$ .

${({(\frac{Gm K}{F})}^{\frac{1}{2}})}^{2} = R^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(\frac{Gm K}{F})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(\frac{Gm K}{F})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(\frac{Gm K}{F})}^{\frac{1}{2} \cdot 2} = R^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(\frac{Gm K}{F})}^{\frac{1}{2} \cdot 2} = R^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(\frac{Gm K}{F})}^{1} = R^{2}$

Step 3.2.1.2

Simplify.

$\frac{Gm K}{F} = R^{2}$

Step 4

Solve for $F$ .

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Step 4.1

Find the LCD of the terms in the equation.

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Step 4.1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$F, 1$

Step 4.1.2

The LCM of one and any expression is the expression.

$F$

Step 4.2

Multiply each term in $\frac{Gm K}{F} = R^{2}$ by $F$ to eliminate the fractions.

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Step 4.2.1

Multiply each term in $\frac{Gm K}{F} = R^{2}$ by $F$ .

$\frac{Gm K}{F} F = R^{2} F$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $F$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{Gm K}{F} F = R^{2} F$

Step 4.2.2.1.2

Rewrite the expression.

$Gm K = R^{2} F$

Step 4.3

Solve the equation.

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Step 4.3.1

Rewrite the equation as $R^{2} F = Gm K$ .

$R^{2} F = Gm K$

Step 4.3.2

Divide each term in $R^{2} F = Gm K$ by $R^{2}$ and simplify.

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Step 4.3.2.1

Divide each term in $R^{2} F = Gm K$ by $R^{2}$ .

$\frac{R^{2} F}{R^{2}} = \frac{Gm K}{R^{2}}$

Step 4.3.2.2

Simplify the left side.

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Step 4.3.2.2.1

Cancel the common factor of $R^{2}$ .

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Step 4.3.2.2.1.1

Cancel the common factor.

$\frac{R^{2} F}{R^{2}} = \frac{Gm K}{R^{2}}$

Step 4.3.2.2.1.2

Divide $F$ by $1$ .

$F = \frac{Gm K}{R^{2}}$

Step 5

Rewrite the expression.

$F = \frac{K}{R^{2}} Gm$