Solve frac{408*frac{sqrt{3}}{2}}{frac{sqrt{2}}{2}}

$$\frac{ 408 \times \frac{ \sqrt{ 3 } }{ 2 } }{ \frac{ \sqrt{ 2 } }{ 2 } }$$

Evaluate

$$204\sqrt{6}\approx 499.695907528$$

Solution Steps

Cancel out 2, the greatest common factor in 408 and 2.

$$\frac{204\sqrt{3}}{\frac{\sqrt{2}}{2}}$$

Divide 204\sqrt{3} by \frac{\sqrt{2}}{2} by multiplying 204\sqrt{3} by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{204\sqrt{3}\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{204\sqrt{3}\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{204\sqrt{3}\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{204\sqrt{3}\times 2\sqrt{2}}{2}$$

Multiply 204 and 2 to get 408.

$$\frac{408\sqrt{3}\sqrt{2}}{2}$$

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

$$\frac{408\sqrt{6}}{2}$$

Divide 408\sqrt{6} by 2 to get 204\sqrt{6}.

$$204\sqrt{6}$$