Solve frac{sqrt{36}}{3}+sqrt{2/81}

$$\frac { \sqrt { 36 } } { 3 } + \sqrt { \frac { 2 } { 81 } }$$

Evaluate

$$\frac{\sqrt{2}}{9}+2\approx 2.15713484$$

Short Solution Steps

Calculate the square root of 36 and get 6.

$$\frac{6}{3}+\sqrt{\frac{2}{81}}$$

Divide 6 by 3 to get 2.

$$2+\sqrt{\frac{2}{81}}$$

Rewrite the square root of the division \sqrt{\frac{2}{81}} as the division of square roots \frac{\sqrt{2}}{\sqrt{81}}.

$$2+\frac{\sqrt{2}}{\sqrt{81}}$$

Calculate the square root of 81 and get 9.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{9}{9}.

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

Since \frac{2\times 9}{9} and \frac{\sqrt{2}}{9} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\times 9+\sqrt{2}.

$$\frac{18+\sqrt{2}}{9}$$

Factor

$$\frac{\sqrt{2} + 18}{9} = 2.1571348402636774$$