Solve (-3)^2-sqrt{21/4}+sqrt[3]{-27}

$$( - 3 ) ^ { 2 } - \sqrt { 2 \frac { 1 } { 4 } } + \sqrt[ 3 ] { - 27 }$$

Evaluate

$$\frac{9}{2}=4.5$$

Solution Steps

Calculate -3 to the power of 2 and get 9.

$$9-\sqrt{\frac{2\times 4+1}{4}}+\sqrt[3]{-27}$$

Multiply 2 and 4 to get 8.

$$9-\sqrt{\frac{8+1}{4}}+\sqrt[3]{-27}$$

Add 8 and 1 to get 9.

$$9-\sqrt{\frac{9}{4}}+\sqrt[3]{-27}$$

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.

$$9-\frac{3}{2}+\sqrt[3]{-27}$$

Subtract \frac{3}{2} from 9 to get \frac{15}{2}.

$$\frac{15}{2}+\sqrt[3]{-27}$$

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

$$\frac{15}{2}-3$$

Subtract 3 from \frac{15}{2} to get \frac{9}{2}.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$