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

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

Evaluate

$$\frac{\sqrt{2}}{9}+2\sqrt{3}\approx 3.621236455$$

Short Solution Steps

Divide 36 by 3 to get 12.

$$\sqrt{12}+\sqrt{\frac{2}{81}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

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

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

Calculate the square root of 81 and get 9.

$$2\sqrt{3}+\frac{\sqrt{2}}{9}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2\sqrt{3} times \frac{9}{9}.

$$\frac{9\times 2\sqrt{3}}{9}+\frac{\sqrt{2}}{9}$$

Since \frac{9\times 2\sqrt{3}}{9} and \frac{\sqrt{2}}{9} have the same denominator, add them by adding their numerators.

$$\frac{9\times 2\sqrt{3}+\sqrt{2}}{9}$$

Do the multiplications in 9\times 2\sqrt{3}+\sqrt{2}.

$$\frac{18\sqrt{3}+\sqrt{2}}{9}$$