Solve frac{sqrt[3]{2^3}}{sqrt{2}}

$$\frac { \sqrt[ 3 ] { 2 ^ { 3 } } } { \sqrt { 2 } }$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$\frac{\sqrt[3]{8}}{\sqrt{2}}$$

Calculate \sqrt[3]{8} and get 2.

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

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 and 2.

$$\sqrt{2}$$