Solve sqrt{frac{sqrt{100}}{5}+sqrt{50/18}-2/3}

$$\sqrt { \frac { \sqrt { 100 } } { 5 } + \sqrt { \frac { 50 } { 18 } } - \frac { 2 } { 3 } }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Calculate the square root of 100 and get 10.

$$\sqrt{\frac{10}{5}+\sqrt{\frac{50}{18}}-\frac{2}{3}}$$

Divide 10 by 5 to get 2.

$$\sqrt{2+\sqrt{\frac{50}{18}}-\frac{2}{3}}$$

Reduce the fraction \frac{50}{18} to lowest terms by extracting and canceling out 2.

$$\sqrt{2+\sqrt{\frac{25}{9}}-\frac{2}{3}}$$

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.

$$\sqrt{2+\frac{5}{3}-\frac{2}{3}}$$

Convert 2 to fraction \frac{6}{3}.

$$\sqrt{\frac{6}{3}+\frac{5}{3}-\frac{2}{3}}$$

Since \frac{6}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{6+5}{3}-\frac{2}{3}}$$

Add 6 and 5 to get 11.

$$\sqrt{\frac{11}{3}-\frac{2}{3}}$$

Since \frac{11}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{11-2}{3}}$$

Subtract 2 from 11 to get 9.

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

Divide 9 by 3 to get 3.

$$\sqrt{3}$$