Solve frac{4sqrt{6}}{frac{sqrt{2}}{2}}

$$\frac { 4 \sqrt { 6 } } { \frac { \sqrt { 2 } } { 2 } }$$

Evaluate

$$8\sqrt{3}\approx 13.856406461$$

Solution Steps

Divide 4\sqrt{6} by \frac{\sqrt{2}}{2} by multiplying 4\sqrt{6} by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{4\sqrt{6}\times 2}{\sqrt{2}}$$

Multiply 4 and 2 to get 8.

$$\frac{8\sqrt{6}}{\sqrt{2}}$$

Rationalize the denominator of \frac{8\sqrt{6}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{8\sqrt{6}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{8\sqrt{6}\sqrt{2}}{2}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$\frac{8\sqrt{2}\sqrt{3}\sqrt{2}}{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{8\times 2\sqrt{3}}{2}$$

Cancel out 2 and 2.

$$8\sqrt{3}$$