Solve 64/9/16sqrt{2/9}

$$\frac { \frac { 64 } { 9 } } { \frac { 16 \sqrt { 2 } } { 9 } }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Divide \frac{64}{9} by \frac{16\sqrt{2}}{9} by multiplying \frac{64}{9} by the reciprocal of \frac{16\sqrt{2}}{9}.

$$\frac{64\times 9}{9\times 16\sqrt{2}}$$

Cancel out 9\times 16 in both numerator and denominator.

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

Rationalize the denominator of \frac{4}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{4\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

Divide 4\sqrt{2} by 2 to get 2\sqrt{2}.

$$2\sqrt{2}$$