Solve f(x)=x^3/sqrt{15}+12*sqrt{x}

$$f ( x ) = \frac { x ^ { 3 } } { \sqrt { 15 } } + 12 \cdot \sqrt { x }$$

Factor

$$\frac{\sqrt{x}\left(\sqrt{15}x^{\frac{5}{2}}+180\right)}{15}$$

Solution Steps

Rationalize the denominator of \frac{x^{3}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$factor(\frac{x^{3}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}+12\sqrt{x})$$

The square of \sqrt{15} is 15.

$$factor(\frac{x^{3}\sqrt{15}}{15}+12\sqrt{x})$$

Factor out \frac{1}{15}.

$$\frac{x^{3}\sqrt{15}+180\sqrt{x}}{15}$$

Consider x^{3}\sqrt{15}+180\sqrt{x}. Factor out \sqrt{x}.

$$\sqrt{x}\left(x^{\frac{5}{2}}\sqrt{15}+180\right)$$

Rewrite the complete factored expression.

$$\frac{\sqrt{x}\left(x^{\frac{5}{2}}\sqrt{15}+180\right)}{15}$$

Evaluate

$$\frac{\sqrt{15}x^{3}}{15}+12\sqrt{x}$$