Simplify 2 square root of 3(3 square root of 3+4 square root of 3)

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

Add $3 \sqrt{3}$ and $4 \sqrt{3}$ .

$2 \sqrt{3} (7 \sqrt{3})$

Multiply $2 \sqrt{3} (7 \sqrt{3})$ .

Multiply $7$ by $2$ .

$14 \sqrt{3} \sqrt{3}$

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

$14 ({\sqrt{3}}^{1} \sqrt{3})$

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

$14 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

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

$14 {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

$14 {\sqrt{3}}^{2}$

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

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

$14 {(3^{\frac{1}{2}})}^{2}$

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

$14 \cdot 3^{\frac{1}{2} \cdot 2}$

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

$14 \cdot 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$14 \cdot 3^{\frac{2}{2}}$

Rewrite the expression.

$14 \cdot 3^{1}$

Evaluate the exponent.

$14 \cdot 3$

Multiply $14$ by $3$ .

$42$