Solve 2/9*3/sqrt{2}

$$\frac { 2 } { 9 } \cdot \frac { 3 } { \sqrt { 2 } }$$

Evaluate

$$\frac{\sqrt{2}}{3}\approx 0.471404521$$

Solution Steps

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

$$\frac{2}{9}\times \frac{3\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{2}{9}\times \frac{3\sqrt{2}}{2}$$

Multiply \frac{2}{9} times \frac{3\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 3\sqrt{2}}{9\times 2}$$

Cancel out 2\times 3 in both numerator and denominator.

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