Solve frac{4sqrt{8}*2}{sqrt{3}}

$$\frac { 4 \sqrt { 8 } \cdot 2 } { \sqrt { 3 } }$$

Evaluate

$$\frac{16\sqrt{6}}{3}\approx 13.063945295$$

Solution Steps

Multiply 2 and 4 to get 8.

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

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

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

Multiply 8 and 2 to get 16.

$$\frac{16\sqrt{2}}{\sqrt{3}}$$

Rationalize the denominator of \frac{16\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{16\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{16\sqrt{2}\sqrt{3}}{3}$$

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

$$\frac{16\sqrt{6}}{3}$$