Solve 2sqrt{3}(sqrt{12}+sqrt{3})div2

$$2 \sqrt { 3 } ( \sqrt { 12 } + \sqrt { 3 } ) \div 2$$

Evaluate

$$9$$

Solution Steps

Cancel out 2 and 2.

$$\sqrt{3}\left(\sqrt{12}+\sqrt{3}\right)$$

Use the distributive property to multiply \sqrt{3} by \sqrt{12}+\sqrt{3}.

$$\sqrt{3}\sqrt{12}+\left(\sqrt{3}\right)^{2}$$

Factor 12=3\times 4. Rewrite the square root of the product \sqrt{3\times 4} as the product of square roots \sqrt{3}\sqrt{4}.

$$\sqrt{3}\sqrt{3}\sqrt{4}+\left(\sqrt{3}\right)^{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$3\sqrt{4}+\left(\sqrt{3}\right)^{2}$$

Calculate the square root of 4 and get 2.

$$3\times 2+\left(\sqrt{3}\right)^{2}$$

Multiply 3 and 2 to get 6.

$$6+\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$6+3$$

Add 6 and 3 to get 9.

$$9$$

Factor

$$3^{2}$$