Solve -sqrt{(-2)^2}-sqrt{125/144}+2/5*sqrt[3]{-125}=

$$- \sqrt { ( - 2 ) ^ { 2 } } - \sqrt { 1 \frac { 25 } { 144 } } + \frac { 2 } { 5 } \times \sqrt[ 3 ] { - 125 } =$$

Evaluate

$$-\frac{61}{12}\approx -5.083333333$$

Solution Steps

Calculate -2 to the power of 2 and get 4.

$$-\sqrt{4}-\sqrt{\frac{1\times 144+25}{144}}+\frac{2}{5}\sqrt[3]{-125}$$

Calculate the square root of 4 and get 2.

$$-2-\sqrt{\frac{1\times 144+25}{144}}+\frac{2}{5}\sqrt[3]{-125}$$

Multiply 1 and 144 to get 144.

$$-2-\sqrt{\frac{144+25}{144}}+\frac{2}{5}\sqrt[3]{-125}$$

Add 144 and 25 to get 169.

$$-2-\sqrt{\frac{169}{144}}+\frac{2}{5}\sqrt[3]{-125}$$

Rewrite the square root of the division \frac{169}{144} as the division of square roots \frac{\sqrt{169}}{\sqrt{144}}. Take the square root of both numerator and denominator.

$$-2-\frac{13}{12}+\frac{2}{5}\sqrt[3]{-125}$$

Subtract \frac{13}{12} from -2 to get -\frac{37}{12}.

$$-\frac{37}{12}+\frac{2}{5}\sqrt[3]{-125}$$

Calculate \sqrt[3]{-125} and get -5.

$$-\frac{37}{12}+\frac{2}{5}\left(-5\right)$$

Multiply \frac{2}{5} and -5 to get -2.

$$-\frac{37}{12}-2$$

Subtract 2 from -\frac{37}{12} to get -\frac{61}{12}.

$$-\frac{61}{12}$$

Factor

$$-\frac{61}{12} = -5\frac{1}{12} = -5.083333333333333$$