Solve (4)2/sqrt{2}+3/sqrt{3}

$$( 4 ) \frac { 2 } { \sqrt { 2 } } + \frac { 3 } { \sqrt { 3 } }$$

Evaluate

$$\sqrt{3}+4\sqrt{2}\approx 7.388905057$$

Solution Steps

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

$$4\times \frac{2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\frac{3}{\sqrt{3}}$$

The square of \sqrt{2} is 2.

$$4\times \frac{2\sqrt{2}}{2}+\frac{3}{\sqrt{3}}$$

Cancel out 2 and 2.

$$4\sqrt{2}+\frac{3}{\sqrt{3}}$$

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

$$4\sqrt{2}+\frac{3\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$4\sqrt{2}+\frac{3\sqrt{3}}{3}$$

Cancel out 3 and 3.

$$4\sqrt{2}+\sqrt{3}$$