Solve sqrt{2ab}+(2/3a^2/sqrt{3})

$$\sqrt { 2 a b } + ( \frac { \frac { 2 } { 3 } a ^ { 2 } } { \sqrt { 3 } } )$$

Factor

$$\frac{\sqrt{2}\left(\sqrt{2}\sqrt{3}a^{2}+9\sqrt{ab}\right)}{9}$$

Solution Steps

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

$$factor(\sqrt{2ab}+\frac{\frac{2}{3}a^{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}})$$

The square of \sqrt{3} is 3.

$$factor(\sqrt{2ab}+\frac{\frac{2}{3}a^{2}\sqrt{3}}{3})$$

Divide \frac{2}{3}a^{2}\sqrt{3} by 3 to get \frac{2}{9}a^{2}\sqrt{3}.

$$factor(\sqrt{2ab}+\frac{2}{9}a^{2}\sqrt{3})$$

Factor out \frac{1}{9}.

$$\frac{9\sqrt{2}\sqrt{ab}+2a^{2}\sqrt{3}}{9}$$

Consider 9\sqrt{2}\sqrt{ab}+2a^{2}\sqrt{3}. Factor out \sqrt{2}.

$$\sqrt{2}\left(9\sqrt{ab}+\sqrt{2}a^{2}\sqrt{3}\right)$$

Rewrite the complete factored expression.

$$\frac{\sqrt{2}\left(9\sqrt{ab}+\sqrt{2}a^{2}\sqrt{3}\right)}{9}$$

Evaluate

$$\frac{2\sqrt{3}a^{2}}{9}+\sqrt{2ab}$$