Basic Math Examples

${(\sqrt{12})}^{2}$

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

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Factor $4$ out of $12$ .

${\sqrt{4 (3)}}^{2}$

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

${\sqrt{2^{2} \cdot 3}}^{2}$

Pull terms out from under the radical.

${(2 \sqrt{3})}^{2}$

Simplify the expression.

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Apply the product rule to $2 \sqrt{3}$ .

$2^{2} {\sqrt{3}}^{2}$

Raise $2$ to the power of $2$ .

$4 {\sqrt{3}}^{2}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$4 {(3^{\frac{1}{2}})}^{2}$

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

$4 \cdot 3^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$4 \cdot 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$4 \cdot 3^{\frac{2}{2}}$

Rewrite the expression.

$4 \cdot 3^{1}$

Evaluate the exponent.

$4 \cdot 3$

Multiply $4$ by $3$ .

$12$