Solve frac{3sqrt{6}*7}{frac{3sqrt{5}}{7}}

$$\frac { 3 \sqrt { 6 } \cdot 7 } { \frac { 3 \sqrt { 5 } } { 7 } }$$

Evaluate

$$\frac{49\sqrt{30}}{5}\approx 53.676810636$$

Solution Steps

Multiply 3 and 7 to get 21.

$$\frac{21\sqrt{6}}{\frac{3\sqrt{5}}{7}}$$

Divide 21\sqrt{6} by \frac{3\sqrt{5}}{7} by multiplying 21\sqrt{6} by the reciprocal of \frac{3\sqrt{5}}{7}.

$$\frac{21\sqrt{6}\times 7}{3\sqrt{5}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{7\times 7\sqrt{6}}{\sqrt{5}}$$

Rationalize the denominator of \frac{7\times 7\sqrt{6}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{7\times 7\sqrt{6}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{7\times 7\sqrt{6}\sqrt{5}}{5}$$

Multiply 7 and 7 to get 49.

$$\frac{49\sqrt{6}\sqrt{5}}{5}$$

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{49\sqrt{30}}{5}$$