Solve (1-frac{2sqrt{2}}{3})frac{16sqrt{2}}{27}

$$(1- \frac{ 2 \sqrt{ 2 } }{ 3 } ) \frac{ 16 \sqrt{ 2 } }{ 27 }$$

Evaluate

$$\frac{16\sqrt{2}}{27}-\frac{64}{81}\approx 0.047929025$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3}{3}.

$$\left(\frac{3}{3}-\frac{2\sqrt{2}}{3}\right)\times \frac{16\sqrt{2}}{27}$$

Since \frac{3}{3} and \frac{2\sqrt{2}}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-2\sqrt{2}}{3}\times \frac{16\sqrt{2}}{27}$$

Multiply \frac{3-2\sqrt{2}}{3} times \frac{16\sqrt{2}}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3-2\sqrt{2}\right)\times 16\sqrt{2}}{3\times 27}$$

Multiply 3 and 27 to get 81.

$$\frac{\left(3-2\sqrt{2}\right)\times 16\sqrt{2}}{81}$$

Use the distributive property to multiply 3-2\sqrt{2} by 16.

$$\frac{\left(48-32\sqrt{2}\right)\sqrt{2}}{81}$$

Use the distributive property to multiply 48-32\sqrt{2} by \sqrt{2}.

$$\frac{48\sqrt{2}-32\left(\sqrt{2}\right)^{2}}{81}$$

The square of \sqrt{2} is 2.

$$\frac{48\sqrt{2}-32\times 2}{81}$$

Multiply -32 and 2 to get -64.

$$\frac{48\sqrt{2}-64}{81}$$

Factor

$$\frac{16 {(3 \sqrt{2} - 4)}}{81} = 0.04792902461615519$$