Solve (1*frac{2sqrt{3}}{3})(2+sqrt{3})

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

Evaluate

$$\frac{4\sqrt{3}}{3}+2\approx 4.309401077$$

Solution Steps

Express 1\times \frac{2\sqrt{3}}{3} as a single fraction.

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

Express \frac{2\sqrt{3}}{3}\left(2+\sqrt{3}\right) as a single fraction.

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

Use the distributive property to multiply 2\sqrt{3} by 2+\sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{4\sqrt{3}+2\times 3}{3}$$

Multiply 2 and 3 to get 6.

$$\frac{4\sqrt{3}+6}{3}$$