Solve 1/8-5/2sqrt[3]{-1/125}+sqrt[3]{-343}-7(1-sqrt{2})

$$\frac { 1 } { 8 } - \frac { 5 } { 2 } \sqrt[ 3 ] { - \frac { 1 } { 125 } } + \sqrt[ 3 ] { - 343 } - 7 ( 1 - \sqrt { 2 } )$$

Evaluate

$$7\sqrt{2}-\frac{107}{8}\approx -3.475505063$$

Solution Steps

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

$$\frac{1}{8}-\frac{5}{2}\left(-\frac{1}{5}\right)+\sqrt[3]{-343}-7\left(1-\sqrt{2}\right)$$

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

$$\frac{1}{8}+\frac{1}{2}+\sqrt[3]{-343}-7\left(1-\sqrt{2}\right)$$

Add \frac{1}{8} and \frac{1}{2} to get \frac{5}{8}.

$$\frac{5}{8}+\sqrt[3]{-343}-7\left(1-\sqrt{2}\right)$$

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

$$\frac{5}{8}-7-7\left(1-\sqrt{2}\right)$$

Subtract 7 from \frac{5}{8} to get -\frac{51}{8}.

$$-\frac{51}{8}-7\left(1-\sqrt{2}\right)$$

Use the distributive property to multiply -7 by 1-\sqrt{2}.

$$-\frac{51}{8}-7+7\sqrt{2}$$

Subtract 7 from -\frac{51}{8} to get -\frac{107}{8}.

$$-\frac{107}{8}+7\sqrt{2}$$

Factor

$$\frac{56 \sqrt{2} - 107}{8} = -3.4755050633883346$$