Solve frac{9sqrt{3}}{2}*1/3sqrt{7}

$$\frac { 9 \sqrt { 3 } } { 2 } \times \frac { 1 } { 3 \sqrt { 7 } }$$

Evaluate

$$\frac{3\sqrt{21}}{14}\approx 0.981980506$$

Solution Steps

Rationalize the denominator of \frac{1}{3\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{9\sqrt{3}}{2}\times \frac{\sqrt{7}}{3\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{9\sqrt{3}}{2}\times \frac{\sqrt{7}}{3\times 7}$$

Multiply 3 and 7 to get 21.

$$\frac{9\sqrt{3}}{2}\times \frac{\sqrt{7}}{21}$$

Multiply \frac{9\sqrt{3}}{2} times \frac{\sqrt{7}}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\sqrt{3}\sqrt{7}}{2\times 21}$$

Cancel out 3 in both numerator and denominator.

$$\frac{3\sqrt{3}\sqrt{7}}{2\times 7}$$

To multiply \sqrt{3} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{3\sqrt{21}}{2\times 7}$$

Multiply 2 and 7 to get 14.

$$\frac{3\sqrt{21}}{14}$$