Solve sqrt{(-1/3-(-11/9))^2}

$$\sqrt { ( \frac { - 1 } { 3 } - ( \frac { - 11 } { 9 } ) ) ^ { 2 } }$$

Evaluate

$$\frac{8}{9}\approx 0.888888889$$

Solution Steps

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$\sqrt{\left(-\frac{1}{3}-\frac{-11}{9}\right)^{2}}$$

Fraction \frac{-11}{9} can be rewritten as -\frac{11}{9} by extracting the negative sign.

$$\sqrt{\left(-\frac{1}{3}-\left(-\frac{11}{9}\right)\right)^{2}}$$

The opposite of -\frac{11}{9} is \frac{11}{9}.

$$\sqrt{\left(-\frac{1}{3}+\frac{11}{9}\right)^{2}}$$

Add -\frac{1}{3} and \frac{11}{9} to get \frac{8}{9}.

$$\sqrt{\left(\frac{8}{9}\right)^{2}}$$

Calculate \frac{8}{9} to the power of 2 and get \frac{64}{81}.

$$\sqrt{\frac{64}{81}}$$

Rewrite the square root of the division \frac{64}{81} as the division of square roots \frac{\sqrt{64}}{\sqrt{81}}. Take the square root of both numerator and denominator.

$$\frac{8}{9}$$

Factor

$$\frac{2 ^ {3}}{3 ^ {2}} = 0.8888888888888888$$