Solve frac{14*frac{5sqrt{3}}{14}}{frac{sqrt{2}}{2}}

$$\frac { 14 \times \frac { 5 \sqrt { 3 } } { 14 } } { \frac { \sqrt { 2 } } { 2 } }$$

Evaluate

$$5\sqrt{6}\approx 12.247448714$$

Solution Steps

Cancel out 14 and 14.

$$\frac{5\sqrt{3}}{\frac{\sqrt{2}}{2}}$$

Divide 5\sqrt{3} by \frac{\sqrt{2}}{2} by multiplying 5\sqrt{3} by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{5\sqrt{3}\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{5\sqrt{3}\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{5\sqrt{3}\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{5\sqrt{3}\times 2\sqrt{2}}{2}$$

Multiply 5 and 2 to get 10.

$$\frac{10\sqrt{3}\sqrt{2}}{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{10\sqrt{6}}{2}$$

Divide 10\sqrt{6} by 2 to get 5\sqrt{6}.

$$5\sqrt{6}$$