Algebra Examples

$\frac{\sqrt{3}}{2} = \frac{\sqrt{12}}{c}$

Step 1

Rewrite the equation as $\frac{\sqrt{12}}{c} = \frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{12}}{c} = \frac{\sqrt{3}}{2}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 2.1.1

Factor $4$ out of $12$ .

$\frac{\sqrt{4 (3)}}{c} = \frac{\sqrt{3}}{2}$

Step 2.1.2

Rewrite $4$ as $2^{2}$ .

$\frac{\sqrt{2^{2} \cdot 3}}{c} = \frac{\sqrt{3}}{2}$

Step 2.2

Pull terms out from under the radical.

$\frac{2 \sqrt{3}}{c} = \frac{\sqrt{3}}{2}$

Step 3

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$2 \sqrt{3} \cdot 2 = c \sqrt{3}$

Step 4

Solve the equation for $c$ .

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Step 4.1

Rewrite the equation as $c \sqrt{3} = 2 \sqrt{3} \cdot 2$ .

$c \sqrt{3} = 2 \sqrt{3} \cdot 2$

Step 4.2

Multiply $2$ by $2$ .

$c \sqrt{3} = 4 \sqrt{3}$

Step 4.3

Divide each term in $c \sqrt{3} = 4 \sqrt{3}$ by $\sqrt{3}$ and simplify.

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Step 4.3.1

Divide each term in $c \sqrt{3} = 4 \sqrt{3}$ by $\sqrt{3}$ .

$\frac{c \sqrt{3}}{\sqrt{3}} = \frac{4 \sqrt{3}}{\sqrt{3}}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $\sqrt{3}$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{c \sqrt{3}}{\sqrt{3}} = \frac{4 \sqrt{3}}{\sqrt{3}}$

Step 4.3.2.1.2

Divide $c$ by $1$ .

$c = \frac{4 \sqrt{3}}{\sqrt{3}}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $\sqrt{3}$ .

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Step 4.3.3.1.1

Cancel the common factor.

$c = \frac{4 \sqrt{3}}{\sqrt{3}}$

Step 4.3.3.1.2

Divide $4$ by $1$ .

$c = 4$