Solve (-3)^2-sqrt{71/2}+sqrt[3]{-27}

$$( - 3 ) ^ { 2 } - \sqrt { 7 \frac { 1 } { 2 } } + \sqrt[ 3 ] { - 27 }$$

Evaluate

$$-\frac{\sqrt{30}}{2}+6\approx 3.261387212$$

Short Solution Steps

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

$$9-\sqrt{\frac{7\times 2+1}{2}}+\sqrt[3]{-27}$$

Multiply 7 and 2 to get 14.

$$9-\sqrt{\frac{14+1}{2}}+\sqrt[3]{-27}$$

Add 14 and 1 to get 15.

$$9-\sqrt{\frac{15}{2}}+\sqrt[3]{-27}$$

Rewrite the square root of the division \sqrt{\frac{15}{2}} as the division of square roots \frac{\sqrt{15}}{\sqrt{2}}.

$$9-\frac{\sqrt{15}}{\sqrt{2}}+\sqrt[3]{-27}$$

Rationalize the denominator of \frac{\sqrt{15}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$9-\frac{\sqrt{15}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\sqrt[3]{-27}$$

The square of \sqrt{2} is 2.

$$9-\frac{\sqrt{15}\sqrt{2}}{2}+\sqrt[3]{-27}$$

To multiply \sqrt{15} and \sqrt{2}, multiply the numbers under the square root.

$$9-\frac{\sqrt{30}}{2}+\sqrt[3]{-27}$$

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

$$9-\frac{\sqrt{30}}{2}-3$$

Subtract 3 from 9 to get 6.

$$6-\frac{\sqrt{30}}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{2}{2}.

$$\frac{6\times 2}{2}-\frac{\sqrt{30}}{2}$$

Since \frac{6\times 2}{2} and \frac{\sqrt{30}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6\times 2-\sqrt{30}}{2}$$

Do the multiplications in 6\times 2-\sqrt{30}.

$$\frac{12-\sqrt{30}}{2}$$