Solve 8/7:-sqrt[3]{8/729}-1/2sqrt[3]{-64}+sqrt{17/9+1}=

$$\frac { 8 } { 7 } : - \sqrt[ 3 ] { \frac { 8 } { 729 } } - \frac { 1 } { 2 } \sqrt[ 3 ] { - 64 } + \sqrt { 1 \frac { 7 } { 9 } + 1 } =$$

Evaluate

$$-\frac{31}{21}\approx -1.476190476$$

Solution Steps

Calculate \sqrt[3]{\frac{8}{729}} and get \frac{2}{9}.

$$\frac{\frac{8}{7}}{-\frac{2}{9}}-\frac{1}{2}\sqrt[3]{-64}+\sqrt{\frac{1\times 9+7}{9}+1}$$

Divide \frac{8}{7} by -\frac{2}{9} by multiplying \frac{8}{7} by the reciprocal of -\frac{2}{9}.

$$\frac{8}{7}\left(-\frac{9}{2}\right)-\frac{1}{2}\sqrt[3]{-64}+\sqrt{\frac{1\times 9+7}{9}+1}$$

Multiply \frac{8}{7} and -\frac{9}{2} to get -\frac{36}{7}.

$$-\frac{36}{7}-\frac{1}{2}\sqrt[3]{-64}+\sqrt{\frac{1\times 9+7}{9}+1}$$

Calculate \sqrt[3]{-64} and get -4.

$$-\frac{36}{7}-\frac{1}{2}\left(-4\right)+\sqrt{\frac{1\times 9+7}{9}+1}$$

Multiply -\frac{1}{2} and -4 to get 2.

$$-\frac{36}{7}+2+\sqrt{\frac{1\times 9+7}{9}+1}$$

Add -\frac{36}{7} and 2 to get -\frac{22}{7}.

$$-\frac{22}{7}+\sqrt{\frac{1\times 9+7}{9}+1}$$

Multiply 1 and 9 to get 9.

$$-\frac{22}{7}+\sqrt{\frac{9+7}{9}+1}$$

Add 9 and 7 to get 16.

$$-\frac{22}{7}+\sqrt{\frac{16}{9}+1}$$

Add \frac{16}{9} and 1 to get \frac{25}{9}.

$$-\frac{22}{7}+\sqrt{\frac{25}{9}}$$

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.

$$-\frac{22}{7}+\frac{5}{3}$$

Add -\frac{22}{7} and \frac{5}{3} to get -\frac{31}{21}.

$$-\frac{31}{21}$$

Factor

$$-\frac{31}{21} = -1\frac{10}{21} = -1.4761904761904763$$