Solve sqrt{(1/9)}+2/1-sqrt{(frac{1{9})}}

$$\sqrt { ( \frac { 1 } { 9 } ) } + \frac { 2 } { 1 - \sqrt { ( \frac { 1 } { 9 } ) } }$$

Evaluate

$$\frac{10}{3}\approx 3.333333333$$

Solution Steps

Rewrite the square root of the division \frac{1}{9} as the division of square roots \frac{\sqrt{1}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{1}{3}+\frac{2}{1-\sqrt{\frac{1}{9}}}$$

Rewrite the square root of the division \frac{1}{9} as the division of square roots \frac{\sqrt{1}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{1}{3}+\frac{2}{1-\frac{1}{3}}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{1}{3}+\frac{2}{\frac{3}{3}-\frac{1}{3}}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}+\frac{2}{\frac{3-1}{3}}$$

Subtract 1 from 3 to get 2.

$$\frac{1}{3}+\frac{2}{\frac{2}{3}}$$

Divide 2 by \frac{2}{3} by multiplying 2 by the reciprocal of \frac{2}{3}.

$$\frac{1}{3}+2\times \frac{3}{2}$$

Cancel out 2 and 2.

$$\frac{1}{3}+3$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{1}{3}+\frac{9}{3}$$

Since \frac{1}{3} and \frac{9}{3} have the same denominator, add them by adding their numerators.

$$\frac{1+9}{3}$$

Add 1 and 9 to get 10.

$$\frac{10}{3}$$

Factor

$$\frac{2 \cdot 5}{3} = 3\frac{1}{3} = 3.3333333333333335$$