Solve (1/3-1)^2/sqrt{frac{11{25}+1}}*(-12)

$$\frac { ( \frac { 1 } { 3 } - 1 ) ^ { 2 } } { \sqrt { \frac { 11 } { 25 } + 1 } } \cdot ( - 12 )$$

Evaluate

$$-\frac{40}{9}\approx -4.444444444$$

Solution Steps

Subtract 1 from \frac{1}{3} to get -\frac{2}{3}.

$$\frac{\left(-\frac{2}{3}\right)^{2}}{\sqrt{\frac{11}{25}+1}}\left(-12\right)$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{\frac{4}{9}}{\sqrt{\frac{11}{25}+1}}\left(-12\right)$$

Add \frac{11}{25} and 1 to get \frac{36}{25}.

$$\frac{\frac{4}{9}}{\sqrt{\frac{36}{25}}}\left(-12\right)$$

Rewrite the square root of the division \frac{36}{25} as the division of square roots \frac{\sqrt{36}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{\frac{4}{9}}{\frac{6}{5}}\left(-12\right)$$

Divide \frac{4}{9} by \frac{6}{5} by multiplying \frac{4}{9} by the reciprocal of \frac{6}{5}.

$$\frac{4}{9}\times \frac{5}{6}\left(-12\right)$$

Multiply \frac{4}{9} and \frac{5}{6} to get \frac{10}{27}.

$$\frac{10}{27}\left(-12\right)$$

Multiply \frac{10}{27} and -12 to get -\frac{40}{9}.

$$-\frac{40}{9}$$

Factor

$$-\frac{40}{9} = -4\frac{4}{9} = -4.444444444444445$$