Solve |sqrt[3]{-1/8}|-(sqrt[3]{0.125})^3+sqrt{6.25}-sqrt[3]{1/64}-1

$$| \sqrt[ 3 ] { - \frac { 1 } { 8 } } | - ( \sqrt[ 3 ] { 0.125 } ) ^ { 3 } + \sqrt { 6.25 } - \sqrt[ 3 ] { \frac { 1 } { 64 } } - 1$$

Evaluate

$$1.625$$

Solution Steps

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

$$|-\frac{1}{2}|-\left(\sqrt[3]{0.125}\right)^{3}+\sqrt{6.25}-\sqrt[3]{\frac{1}{64}}-1$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{1}{2} is \frac{1}{2}.

$$\frac{1}{2}-\left(\sqrt[3]{0.125}\right)^{3}+\sqrt{6.25}-\sqrt[3]{\frac{1}{64}}-1$$

Calculate \sqrt[3]{0.125} and get \frac{1}{2}.

$$\frac{1}{2}-\left(\frac{1}{2}\right)^{3}+\sqrt{6.25}-\sqrt[3]{\frac{1}{64}}-1$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{1}{2}-\frac{1}{8}+\sqrt{6.25}-\sqrt[3]{\frac{1}{64}}-1$$

Subtract \frac{1}{8} from \frac{1}{2} to get \frac{3}{8}.

$$\frac{3}{8}+\sqrt{6.25}-\sqrt[3]{\frac{1}{64}}-1$$

Calculate the square root of 6.25 and get 2.5.

$$\frac{3}{8}+2.5-\sqrt[3]{\frac{1}{64}}-1$$

Add \frac{3}{8} and 2.5 to get \frac{23}{8}.

$$\frac{23}{8}-\sqrt[3]{\frac{1}{64}}-1$$

Calculate \sqrt[3]{\frac{1}{64}} and get \frac{1}{4}.

$$\frac{23}{8}-\frac{1}{4}-1$$

Subtract \frac{1}{4} from \frac{23}{8} to get \frac{21}{8}.

$$\frac{21}{8}-1$$

Subtract 1 from \frac{21}{8} to get \frac{13}{8}.

$$\frac{13}{8}$$

Factor

$$\frac{13}{2 ^ {3}} = 1\frac{5}{8} = 1.625$$