Solve sqrt{2+7/9}-sqrt{1-8/9}

$$\sqrt { 2 + \frac { 7 } { 9 } } - \sqrt { 1 - \frac { 8 } { 9 } }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

Convert 2 to fraction \frac{18}{9}.

$$\sqrt{\frac{18}{9}+\frac{7}{9}}-\sqrt{1-\frac{8}{9}}$$

Since \frac{18}{9} and \frac{7}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{18+7}{9}}-\sqrt{1-\frac{8}{9}}$$

Add 18 and 7 to get 25.

$$\sqrt{\frac{25}{9}}-\sqrt{1-\frac{8}{9}}$$

Rewrite the square root of the division \frac{25}{9} as the division of square roots \frac{\sqrt{25}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{5}{3}-\sqrt{1-\frac{8}{9}}$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{5}{3}-\sqrt{\frac{9}{9}-\frac{8}{9}}$$

Since \frac{9}{9} and \frac{8}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{3}-\sqrt{\frac{9-8}{9}}$$

Subtract 8 from 9 to get 1.

$$\frac{5}{3}-\sqrt{\frac{1}{9}}$$

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.

$$\frac{5}{3}-\frac{1}{3}$$

Since \frac{5}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-1}{3}$$

Subtract 1 from 5 to get 4.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$