Solve 1/1frac{30{9sqrt{3}}}

$$\frac { 1 } { 1 \frac { 30 } { 9 \sqrt { 3 } } }$$

Evaluate

$$\frac{3\sqrt{3}}{10}\approx 0.519615242$$

Solution Steps

Rationalize the denominator of \frac{30}{9\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{1}{1\times \frac{30\sqrt{3}}{9\left(\sqrt{3}\right)^{2}}}$$

The square of \sqrt{3} is 3.

$$\frac{1}{1\times \frac{30\sqrt{3}}{9\times 3}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{1\times \frac{10\sqrt{3}}{3\times 3}}$$

Multiply 3 and 3 to get 9.

$$\frac{1}{1\times \frac{10\sqrt{3}}{9}}$$

Express 1\times \frac{10\sqrt{3}}{9} as a single fraction.

$$\frac{1}{\frac{10\sqrt{3}}{9}}$$

Divide 1 by \frac{10\sqrt{3}}{9} by multiplying 1 by the reciprocal of \frac{10\sqrt{3}}{9}.

$$\frac{9}{10\sqrt{3}}$$

Rationalize the denominator of \frac{9}{10\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{9\sqrt{3}}{10\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{9\sqrt{3}}{10\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{3\sqrt{3}}{10}$$