Solve sqrt{(21/3)^2}-(sqrt{(-22/3)^2})

$$\sqrt { ( 2 \frac { 1 } { 3 } ) ^ { 2 } } - ( \sqrt { ( - 2 \frac { 2 } { 3 } ) ^ { 2 } } )$$

Evaluate

$$-\frac{1}{3}\approx -0.333333333$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\sqrt{\left(\frac{6+1}{3}\right)^{2}}-\sqrt{\left(-\frac{2\times 3+2}{3}\right)^{2}}$$

Add 6 and 1 to get 7.

$$\sqrt{\left(\frac{7}{3}\right)^{2}}-\sqrt{\left(-\frac{2\times 3+2}{3}\right)^{2}}$$

Calculate \frac{7}{3} to the power of 2 and get \frac{49}{9}.

$$\sqrt{\frac{49}{9}}-\sqrt{\left(-\frac{2\times 3+2}{3}\right)^{2}}$$

Rewrite the square root of the division \frac{49}{9} as the division of square roots \frac{\sqrt{49}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{7}{3}-\sqrt{\left(-\frac{2\times 3+2}{3}\right)^{2}}$$

Multiply 2 and 3 to get 6.

$$\frac{7}{3}-\sqrt{\left(-\frac{6+2}{3}\right)^{2}}$$

Add 6 and 2 to get 8.

$$\frac{7}{3}-\sqrt{\left(-\frac{8}{3}\right)^{2}}$$

Calculate -\frac{8}{3} to the power of 2 and get \frac{64}{9}.

$$\frac{7}{3}-\sqrt{\frac{64}{9}}$$

Rewrite the square root of the division \frac{64}{9} as the division of square roots \frac{\sqrt{64}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{7}{3}-\frac{8}{3}$$

Subtract \frac{8}{3} from \frac{7}{3} to get -\frac{1}{3}.

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

Factor

$$-\frac{1}{3} = -0.3333333333333333$$