Simplify square root of 3(4 square root of 3+4)

$\sqrt{3} (4 \sqrt{3} + 4)$

Apply the distributive property.

$\sqrt{3} (4 \sqrt{3}) + \sqrt{3} \cdot 4$

Multiply $\sqrt{3} (4 \sqrt{3})$ .

Raise $\sqrt{3}$ to the power of $1$ .

$4 ({\sqrt{3}}^{1} \sqrt{3}) + \sqrt{3} \cdot 4$

Raise $\sqrt{3}$ to the power of $1$ .

$4 ({\sqrt{3}}^{1} {\sqrt{3}}^{1}) + \sqrt{3} \cdot 4$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 {\sqrt{3}}^{1 + 1} + \sqrt{3} \cdot 4$

Add $1$ and $1$ .

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

Move $4$ to the left of $\sqrt{3}$ .

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

Simplify each term.

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$4 \cdot 3^{1} + 4 \cdot \sqrt{3}$

Evaluate the exponent.

$4 \cdot 3 + 4 \cdot \sqrt{3}$

Multiply $4$ by $3$ .

$12 + 4 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$12 + 4 \sqrt{3}$

Decimal Form:

$18.92820323 \dots$