Solve (1/sqrt{2}*8sqrt{2}*2/3)*1/2

$$( \frac { 1 } { \sqrt { 2 } } \times 8 \sqrt { 2 } \times \frac { 2 } { 3 } ) \times \frac { 1 } { 2 }$$

Evaluate

$$\frac{8}{3}\approx 2.666666667$$

Solution Steps

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

$$8\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\sqrt{2}\times \frac{2}{3}\times \frac{1}{2}$$

The square of \sqrt{2} is 2.

$$8\times \frac{\sqrt{2}}{2}\sqrt{2}\times \frac{2}{3}\times \frac{1}{2}$$

Express 8\times \frac{2}{3} as a single fraction.

$$\frac{8\times 2}{3}\times \frac{\sqrt{2}}{2}\sqrt{2}\times \frac{1}{2}$$

Multiply 8 and 2 to get 16.

$$\frac{16}{3}\times \frac{\sqrt{2}}{2}\sqrt{2}\times \frac{1}{2}$$

Multiply \frac{16}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\times 1}{3\times 2}\times \frac{\sqrt{2}}{2}\sqrt{2}$$

Do the multiplications in the fraction \frac{16\times 1}{3\times 2}.

$$\frac{16}{6}\times \frac{\sqrt{2}}{2}\sqrt{2}$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

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

Multiply \frac{8}{3} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

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

Express \frac{4\sqrt{2}}{3}\sqrt{2} as a single fraction.

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

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

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

Multiply 4 and 2 to get 8.

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

Factor

$$\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2.6666666666666665$$