Solve frac{8sqrt{3}}{sqrt{6}}

$$\frac { 8 \sqrt { 3 } } { \sqrt { 6 } }$$

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

Solution Steps

Rationalize the denominator of \frac{8\sqrt{3}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{8\sqrt{3}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{8\sqrt{3}\sqrt{6}}{6}$$

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

$$\frac{8\sqrt{3}\sqrt{3}\sqrt{2}}{6}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{8\times 3\sqrt{2}}{6}$$

Multiply 8 and 3 to get 24.

$$\frac{24\sqrt{2}}{6}$$

Divide 24\sqrt{2} by 6 to get 4\sqrt{2}.

$$4\sqrt{2}$$