Finite Math Examples

$A = \sqrt{\frac{2}{c p}}$

Step 1

Rewrite the equation as $\sqrt{\frac{2}{c p}} = A$ .

$\sqrt{\frac{2}{c p}} = A$

Step 2

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

${\sqrt{\frac{2}{c p}}}^{2} = A^{2}$

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 $\sqrt{\frac{2}{c p}}$ as ${(\frac{2}{c p})}^{\frac{1}{2}}$ .

${({(\frac{2}{c p})}^{\frac{1}{2}})}^{2} = A^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(\frac{2}{c p})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(\frac{2}{c p})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(\frac{2}{c p})}^{\frac{1}{2} \cdot 2} = A^{2}$

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.

${(\frac{2}{c p})}^{\frac{1}{2} \cdot 2} = A^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(\frac{2}{c p})}^{1} = A^{2}$

Step 3.2.1.2

Simplify.

$\frac{2}{c p} = A^{2}$

Step 4

Solve for $p$ .

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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.

$c p, 1$

Step 4.1.2

The LCM of one and any expression is the expression.

$c p$

Step 4.2

Multiply each term in $\frac{2}{c p} = A^{2}$ by $c p$ to eliminate the fractions.

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Step 4.2.1

Multiply each term in $\frac{2}{c p} = A^{2}$ by $c p$ .

$\frac{2}{c p} (c p) = A^{2} (c p)$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $c p$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2}{c p} (c p) = A^{2} (c p)$

Step 4.2.2.1.2

Rewrite the expression.

$2 = A^{2} (c p)$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Remove parentheses.

$2 = A^{2} c p$

Step 4.3

Solve the equation.

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Step 4.3.1

Rewrite the equation as $A^{2} c p = 2$ .

$A^{2} c p = 2$

Step 4.3.2

Divide each term in $A^{2} c p = 2$ by $A^{2} c$ and simplify.

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Step 4.3.2.1

Divide each term in $A^{2} c p = 2$ by $A^{2} c$ .

$\frac{A^{2} c p}{A^{2} c} = \frac{2}{A^{2} c}$

Step 4.3.2.2

Simplify the left side.

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Step 4.3.2.2.1

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

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Step 4.3.2.2.1.1

Cancel the common factor.

$\frac{A^{2} c p}{A^{2} c} = \frac{2}{A^{2} c}$

Step 4.3.2.2.1.2

Rewrite the expression.

$\frac{c p}{c} = \frac{2}{A^{2} c}$

Step 4.3.2.2.2

Cancel the common factor of $c$ .

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Step 4.3.2.2.2.1

Cancel the common factor.

$\frac{c p}{c} = \frac{2}{A^{2} c}$

Step 4.3.2.2.2.2

Divide $p$ by $1$ .

$p = \frac{2}{A^{2} c}$