Solve (5)sqrt[3]{7/8-1}+sqrt{1/64}-sqrt[3]{1-37/64}-sqrt{1/4}

$$( 5 ) \sqrt[ 3 ] { \frac { 7 } { 8 } - 1 } + \sqrt { \frac { 1 } { 64 } } - \sqrt[ 3 ] { 1 - \frac { 37 } { 64 } } - \sqrt { \frac { 1 } { 4 } }$$

Evaluate

$$-\frac{29}{8}=-3.625$$

Solution Steps

Subtract 1 from \frac{7}{8} to get -\frac{1}{8}.

$$5\sqrt[3]{-\frac{1}{8}}+\sqrt{\frac{1}{64}}-\sqrt[3]{1-\frac{37}{64}}-\sqrt{\frac{1}{4}}$$

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

$$5\left(-\frac{1}{2}\right)+\sqrt{\frac{1}{64}}-\sqrt[3]{1-\frac{37}{64}}-\sqrt{\frac{1}{4}}$$

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

$$-\frac{5}{2}+\sqrt{\frac{1}{64}}-\sqrt[3]{1-\frac{37}{64}}-\sqrt{\frac{1}{4}}$$

Rewrite the square root of the division \frac{1}{64} as the division of square roots \frac{\sqrt{1}}{\sqrt{64}}. Take the square root of both numerator and denominator.

$$-\frac{5}{2}+\frac{1}{8}-\sqrt[3]{1-\frac{37}{64}}-\sqrt{\frac{1}{4}}$$

Add -\frac{5}{2} and \frac{1}{8} to get -\frac{19}{8}.

$$-\frac{19}{8}-\sqrt[3]{1-\frac{37}{64}}-\sqrt{\frac{1}{4}}$$

Subtract \frac{37}{64} from 1 to get \frac{27}{64}.

$$-\frac{19}{8}-\sqrt[3]{\frac{27}{64}}-\sqrt{\frac{1}{4}}$$

Calculate \sqrt[3]{\frac{27}{64}} and get \frac{3}{4}.

$$-\frac{19}{8}-\frac{3}{4}-\sqrt{\frac{1}{4}}$$

Subtract \frac{3}{4} from -\frac{19}{8} to get -\frac{25}{8}.

$$-\frac{25}{8}-\sqrt{\frac{1}{4}}$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$-\frac{25}{8}-\frac{1}{2}$$

Subtract \frac{1}{2} from -\frac{25}{8} to get -\frac{29}{8}.

$$-\frac{29}{8}$$

Factor

$$-\frac{29}{8} = -3\frac{5}{8} = -3.625$$