Solve 9/sqrt[3]{2}*frac{sqrt[3]{2}}{sqrt{2}}=

$$\frac { 9 } { \sqrt[ 3 ] { 2 } } \cdot \frac { \sqrt[ 3 ] { 2 } } { \sqrt { 2 } } =$$

Evaluate

$$\frac{9\sqrt{2}}{2}\approx 6.363961031$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

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

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

Cancel out \sqrt[3]{2} in both numerator and denominator.

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