Solve frac{sqrt{3}}{2}:frac{sqrt{2}}{8}=?

$$\frac { \sqrt { 3 } } { 2 } : \frac { \sqrt { 2 } } { 8 } = ?$$

Evaluate

$$2\sqrt{6}\approx 4.898979486$$

Solution Steps

Divide \frac{\sqrt{3}}{2} by \frac{\sqrt{2}}{8} by multiplying \frac{\sqrt{3}}{2} by the reciprocal of \frac{\sqrt{2}}{8}.

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

Cancel out 2 in both numerator and denominator.

$$\frac{4\sqrt{3}}{\sqrt{2}}$$

Rationalize the denominator of \frac{4\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{4\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{4\sqrt{3}\sqrt{2}}{2}$$

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

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

Divide 4\sqrt{6} by 2 to get 2\sqrt{6}.

$$2\sqrt{6}$$