Basic Math Examples

$\sqrt{12} = k \sqrt{3}$

Step 1

Rewrite the equation as $k \sqrt{3} = \sqrt{12}$ .

$k \sqrt{3} = \sqrt{12}$

Step 2

Divide each term in $k \sqrt{3} = \sqrt{12}$ by $\sqrt{3}$ and simplify.

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Step 2.1

Divide each term in $k \sqrt{3} = \sqrt{12}$ by $\sqrt{3}$ .

$\frac{k \sqrt{3}}{\sqrt{3}} = \frac{\sqrt{12}}{\sqrt{3}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

Cancel the common factor.

$\frac{k \sqrt{3}}{\sqrt{3}} = \frac{\sqrt{12}}{\sqrt{3}}$

Step 2.2.1.2

Divide $k$ by $1$ .

$k = \frac{\sqrt{12}}{\sqrt{3}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Combine $\sqrt{12}$ and $\sqrt{3}$ into a single radical.

$k = \sqrt{\frac{12}{3}}$

Step 2.3.2

Simplify the expression.

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Step 2.3.2.1

Divide $12$ by $3$ .

$k = \sqrt{4}$

Step 2.3.2.2

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

$k = \sqrt{2^{2}}$

Step 2.3.3

Pull terms out from under the radical, assuming positive real numbers.

$k = 2$