Solve sqrt{21/4}-sqrt[3]{155/8}

$$\sqrt { 2 \frac { 1 } { 4 } } - \sqrt[ 3 ] { 15 \frac { 5 } { 8 } }$$

Evaluate

$$-1$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\sqrt{\frac{8+1}{4}}-\sqrt[3]{\frac{15\times 8+5}{8}}$$

Add 8 and 1 to get 9.

$$\sqrt{\frac{9}{4}}-\sqrt[3]{\frac{15\times 8+5}{8}}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{3}{2}-\sqrt[3]{\frac{15\times 8+5}{8}}$$

Multiply 15 and 8 to get 120.

$$\frac{3}{2}-\sqrt[3]{\frac{120+5}{8}}$$

Add 120 and 5 to get 125.

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

Calculate \sqrt[3]{\frac{125}{8}} and get \frac{5}{2}.

$$\frac{3}{2}-\frac{5}{2}$$

Subtract \frac{5}{2} from \frac{3}{2} to get -1.

$$-1$$

Factor

$$-1$$