Solve 4sqrt{8}*2/5sqrt{1/2}

$$4 \sqrt { 8 } \times \frac { 2 } { 5 } \sqrt { \frac { 1 } { 2 } }$$

Evaluate

$$\frac{16}{5}=3.2$$

Solution Steps

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}.

$$4\times 2\sqrt{2}\times \frac{2}{5}\sqrt{\frac{1}{2}}$$

Multiply 4 and 2 to get 8.

$$8\sqrt{2}\times \frac{2}{5}\sqrt{\frac{1}{2}}$$

Express 8\times \frac{2}{5} as a single fraction.

$$\frac{8\times 2}{5}\sqrt{2}\sqrt{\frac{1}{2}}$$

Multiply 8 and 2 to get 16.

$$\frac{16}{5}\sqrt{2}\sqrt{\frac{1}{2}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$\frac{16}{5}\sqrt{2}\times \frac{\sqrt{1}}{\sqrt{2}}$$

Calculate the square root of 1 and get 1.

$$\frac{16}{5}\sqrt{2}\times \frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{16}{5}\sqrt{2}\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{16}{5}\sqrt{2}\times \frac{\sqrt{2}}{2}$$

Multiply \frac{16}{5} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\sqrt{2}}{5\times 2}\sqrt{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{8\sqrt{2}}{5}\sqrt{2}$$

Express \frac{8\sqrt{2}}{5}\sqrt{2} as a single fraction.

$$\frac{8\sqrt{2}\sqrt{2}}{5}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{8\times 2}{5}$$

Multiply 8 and 2 to get 16.

$$\frac{16}{5}$$

Factor

$$\frac{2 ^ {4}}{5} = 3\frac{1}{5} = 3.2$$