Solve sqrt[3]{1/8}-5/2sqrt[3]{1/125}+sqrt[3]{-343}-sqrt{2-1.75}

$$\sqrt[ 3 ] { \frac { 1 } { 8 } } - \frac { 5 } { 2 } \sqrt[ 3 ] { \frac { 1 } { 125 } } + \sqrt[ 3 ] { - 343 } - \sqrt { 2 - 1.75 }$$

Evaluate

$$-7.5$$

Solution Steps

Calculate \sqrt[3]{\frac{1}{8}} and get \frac{1}{2}.

$$\frac{1}{2}-\frac{5}{2}\sqrt[3]{\frac{1}{125}}+\sqrt[3]{-343}-\sqrt{2-1.75}$$

Calculate \sqrt[3]{\frac{1}{125}} and get \frac{1}{5}.

$$\frac{1}{2}-\frac{5}{2}\times \frac{1}{5}+\sqrt[3]{-343}-\sqrt{2-1.75}$$

Multiply -\frac{5}{2} and \frac{1}{5} to get -\frac{1}{2}.

$$\frac{1}{2}-\frac{1}{2}+\sqrt[3]{-343}-\sqrt{2-1.75}$$

Subtract \frac{1}{2} from \frac{1}{2} to get 0.

$$\sqrt[3]{-343}-\sqrt{2-1.75}$$

Calculate \sqrt[3]{-343} and get -7.

$$-7-\sqrt{2-1.75}$$

Subtract 1.75 from 2 to get 0.25.

$$-7-\sqrt{0.25}$$

Calculate the square root of 0.25 and get 0.5.

$$-7-0.5$$

Subtract 0.5 from -7 to get -7.5.

$$-7.5$$

Factor

$$-7.5$$