Solve frac{sqrt{3}}{3}(frac{30+20sqrt{3}}{3})

$$\frac { \sqrt { 3 } } { 3 } ( \frac { 30 + 20 \sqrt { 3 } } { 3 } )$$

Evaluate

$$\frac{10\left(\sqrt{3}+2\right)}{3}\approx 12.440169359$$

Solution Steps

Multiply \frac{\sqrt{3}}{3} times \frac{30+20\sqrt{3}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{3}\left(30+20\sqrt{3}\right)}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{\sqrt{3}\left(30+20\sqrt{3}\right)}{9}$$

Use the distributive property to multiply \sqrt{3} by 30+20\sqrt{3}.

$$\frac{30\sqrt{3}+20\left(\sqrt{3}\right)^{2}}{9}$$

The square of \sqrt{3} is 3.

$$\frac{30\sqrt{3}+20\times 3}{9}$$

Multiply 20 and 3 to get 60.

$$\frac{30\sqrt{3}+60}{9}$$

Factor

$$\frac{10 {(\sqrt{3} + 2)}}{3} = 12.440169358562924$$