Solve 4/9sqrt{3}30^circ

$$\frac { 4 } { 9 \sqrt { 3 } } 30 ^ { \circ }$$

Evaluate

$$\frac{40\sqrt{3}}{9}\approx 7.698003589$$

Solution Steps

Rationalize the denominator of \frac{4}{9\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$30\times \frac{4\sqrt{3}}{9\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$30\times \frac{4\sqrt{3}}{9\times 3}$$

Multiply 9 and 3 to get 27.

$$30\times \frac{4\sqrt{3}}{27}$$

Express 30\times \frac{4\sqrt{3}}{27} as a single fraction.

$$\frac{30\times 4\sqrt{3}}{27}$$

Multiply 30 and 4 to get 120.

$$\frac{120\sqrt{3}}{27}$$

Divide 120\sqrt{3} by 27 to get \frac{40}{9}\sqrt{3}.

$$\frac{40}{9}\sqrt{3}$$