Simplify (3 square root of 12)^2

${(3 \sqrt{12})}^{2}$

Step 1

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

Factor $4$ out of $12$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Simplify the expression.

Multiply $2$ by $3$ .

${(6 \sqrt{3})}^{2}$

Apply the product rule to $6 \sqrt{3}$ .

$6^{2} {\sqrt{3}}^{2}$

Raise $6$ to the power of $2$ .

$36 {\sqrt{3}}^{2}$

Step 4

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

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

$36 {(3^{\frac{1}{2}})}^{2}$

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

$36 \cdot 3^{\frac{1}{2} \cdot 2}$

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

$36 \cdot 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$36 \cdot 3^{\frac{2}{2}}$

Rewrite the expression.

$36 \cdot 3^{1}$

Evaluate the exponent.

$36 \cdot 3$

Step 5

Multiply $36$ by $3$ .

$108$