Solve frac{sqrt{384}}{sqrt{2}*sqrt{3}}

$$\frac { \sqrt { 384 } } { \sqrt { 2 } \times \sqrt { 3 } }$$

Evaluate

$$8$$

Solution Steps

Factor 384=8^{2}\times 6. Rewrite the square root of the product \sqrt{8^{2}\times 6} as the product of square roots \sqrt{8^{2}}\sqrt{6}. Take the square root of 8^{2}.

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

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

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

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

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

The square of \sqrt{6} is 6.

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

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{8\times 6}{6}$$

Multiply 8 and 6 to get 48.

$$\frac{48}{6}$$

Divide 48 by 6 to get 8.

$$8$$

Factor

$$2^{3}$$