Solve frac{q^{2}}{4}+p^3/27)^frac{1{3}}+(q/2-sqrt{q^2/4+p^3/27}

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

Evaluate

$$\frac{p^{3}}{27}+\frac{q^{2}}{4}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 27 is 108. Multiply \frac{q^{2}}{4} times \frac{27}{27}. Multiply \frac{p^{3}}{27} times \frac{4}{4}.

$$\frac{27q^{2}}{108}+\frac{4p^{3}}{108}$$

Since \frac{27q^{2}}{108} and \frac{4p^{3}}{108} have the same denominator, add them by adding their numerators.

$$\frac{27q^{2}+4p^{3}}{108}$$

Factor

$$\frac{4p^{3}+27q^{2}}{108}$$

Solution Steps

Factor out \frac{1}{108}.

$$\frac{27q^{2}+4p^{3}}{108}$$