Solve sqrt{1/4}-sqrt[3]{-33/8}+sqrt[3]{-125}

$$\sqrt { \frac { 1 } { 4 } } - \sqrt[ 3 ] { - 3 \frac { 3 } { 8 } } + \sqrt[ 3 ] { - 125 }$$

Evaluate

$$-3$$

Solution Steps

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.

$$\frac{1}{2}-\sqrt[3]{-\frac{3\times 8+3}{8}}+\sqrt[3]{-125}$$

Multiply 3 and 8 to get 24.

$$\frac{1}{2}-\sqrt[3]{-\frac{24+3}{8}}+\sqrt[3]{-125}$$

Add 24 and 3 to get 27.

$$\frac{1}{2}-\sqrt[3]{-\frac{27}{8}}+\sqrt[3]{-125}$$

Calculate \sqrt[3]{-\frac{27}{8}} and get -\frac{3}{2}.

$$\frac{1}{2}-\left(-\frac{3}{2}\right)+\sqrt[3]{-125}$$

The opposite of -\frac{3}{2} is \frac{3}{2}.

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

Add \frac{1}{2} and \frac{3}{2} to get 2.

$$2+\sqrt[3]{-125}$$

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

$$2-5$$

Subtract 5 from 2 to get -3.

$$-3$$

Factor

$$-3$$