Solve sqrt{9/4}-sqrt{3}cos30^circ+sqrt[3]{-8}

$$\sqrt { \frac { 9 } { 4 } } - \sqrt { 3 } \cos 30 ^ { \circ } + \sqrt[ 3 ] { - 8 }$$

Evaluate

$$-2$$

Solution Steps

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.

$$\frac{3}{2}-\sqrt{3}\cos(30)+\sqrt[3]{-8}$$

Get the value of \cos(30) from trigonometric values table.

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

Express \sqrt{3}\times \frac{\sqrt{3}}{2} as a single fraction.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Subtract \frac{3}{2} from \frac{3}{2} to get 0.

$$0+\sqrt[3]{-8}$$

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

$$0-2$$

Subtract 2 from 0 to get -2.

$$-2$$