Solve frac{2(5x)^frac{3{2}}+6(5x)^1/2}{3}

$$\frac { 2 ( 5 x ) ^ { \frac { 3 } { 2 } } + 6 ( 5 x ) ^ { 1 / 2 } } { 3 }$$

Factor

$$\frac{2\sqrt{5x}\left(5x+3\right)}{3}$$

Solution Steps

Consider 2\times \left(5x\right)^{\frac{3}{2}}+6\times \left(5x\right)^{\frac{1}{2}}. Factor out 2.

$$2\left(5\sqrt{5}x^{\frac{3}{2}}+3\sqrt{5}\sqrt{x}\right)$$

Consider x^{\frac{3}{2}}\times 5^{\frac{3}{2}}+3\sqrt{5}\sqrt{x}. Factor out \sqrt{x}\sqrt{5}.

$$\sqrt{x}\sqrt{5}\left(5x+3\right)$$

Rewrite the complete factored expression. Simplify.

$$\frac{2\left(5x+3\right)\sqrt{5}\sqrt{x}}{3}$$

Evaluate

$$\frac{2\sqrt{5x}\left(5x+3\right)}{3}$$