Solve 1/3*3/sqrt{2}

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

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

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

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

Cancel out 3 in both numerator and denominator.

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