Solve sqrt[3]{64}-sqrt{81}+sqrt[3]{-1}-sqrt[3]{-2+3/64}

$$\sqrt[ 3 ] { 64 } - \sqrt { 81 } + \sqrt[ 3 ] { - 1 } - \sqrt[ 3 ] { - 2 + \frac { 3 } { 64 } }$$

Evaluate

$$-\frac{19}{4}=-4.75$$

Solution Steps

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

$$4-\sqrt{81}+\sqrt[3]{-1}-\sqrt[3]{-2+\frac{3}{64}}$$

Calculate the square root of 81 and get 9.

$$4-9+\sqrt[3]{-1}-\sqrt[3]{-2+\frac{3}{64}}$$

Subtract 9 from 4 to get -5.

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

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

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

Subtract 1 from -5 to get -6.

$$-6-\sqrt[3]{-2+\frac{3}{64}}$$

Add -2 and \frac{3}{64} to get -\frac{125}{64}.

$$-6-\sqrt[3]{-\frac{125}{64}}$$

Calculate \sqrt[3]{-\frac{125}{64}} and get -\frac{5}{4}.

$$-6-\left(-\frac{5}{4}\right)$$

The opposite of -\frac{5}{4} is \frac{5}{4}.

$$-6+\frac{5}{4}$$

Add -6 and \frac{5}{4} to get -\frac{19}{4}.

$$-\frac{19}{4}$$

Factor

$$-\frac{19}{4} = -4\frac{3}{4} = -4.75$$