Basic Math Examples

$t = \sqrt{\frac{1}{R C}}$

Step 1

Rewrite the equation as $\sqrt{\frac{1}{R C}} = t$ .

$\sqrt{\frac{1}{R C}} = t$

Step 2

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

${\sqrt{\frac{1}{R C}}}^{2} = t^{2}$

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 $\sqrt{\frac{1}{R C}}$ as ${(\frac{1}{R C})}^{\frac{1}{2}}$ .

${({(\frac{1}{R C})}^{\frac{1}{2}})}^{2} = t^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(\frac{1}{R C})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(\frac{1}{R C})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(\frac{1}{R C})}^{\frac{1}{2} \cdot 2} = t^{2}$

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.

${(\frac{1}{R C})}^{\frac{1}{2} \cdot 2} = t^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(\frac{1}{R C})}^{1} = t^{2}$

Step 3.2.1.2

Simplify.

$\frac{1}{R C} = t^{2}$

Step 4

Solve for $R$ .

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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.

$R C, 1$

Step 4.1.2

The LCM of one and any expression is the expression.

$R C$

Step 4.2

Multiply each term in $\frac{1}{R C} = t^{2}$ by $R C$ to eliminate the fractions.

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Step 4.2.1

Multiply each term in $\frac{1}{R C} = t^{2}$ by $R C$ .

$\frac{1}{R C} (R C) = t^{2} (R C)$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $R C$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{1}{R C} (R C) = t^{2} (R C)$

Step 4.2.2.1.2

Rewrite the expression.

$1 = t^{2} (R C)$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Remove parentheses.

$1 = t^{2} R C$

Step 4.3

Solve the equation.

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Step 4.3.1

Rewrite the equation as $t^{2} R C = 1$ .

$t^{2} R C = 1$

Step 4.3.2

Divide each term in $t^{2} R C = 1$ by $t^{2} C$ and simplify.

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Step 4.3.2.1

Divide each term in $t^{2} R C = 1$ by $t^{2} C$ .

$\frac{t^{2} R C}{t^{2} C} = \frac{1}{t^{2} C}$

Step 4.3.2.2

Simplify the left side.

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Step 4.3.2.2.1

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

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Step 4.3.2.2.1.1

Cancel the common factor.

$\frac{t^{2} R C}{t^{2} C} = \frac{1}{t^{2} C}$

Step 4.3.2.2.1.2

Rewrite the expression.

$\frac{R C}{C} = \frac{1}{t^{2} C}$

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.

$\frac{R C}{C} = \frac{1}{t^{2} C}$

Step 4.3.2.2.2.2

Divide $R$ by $1$ .

$R = \frac{1}{t^{2} C}$