Simplify ( square root of 12x+15x^2)/( square root of 3x)

$\frac{\sqrt{12 x + 15 x^{2}}}{\sqrt{3 x}}$

Step 1

Factor $3 x$ out of $12 x + 15 x^{2}$ .

Factor $3 x$ out of $12 x$ .

$\frac{\sqrt{3 x (4) + 15 x^{2}}}{\sqrt{3 x}}$

Factor $3 x$ out of $15 x^{2}$ .

$\frac{\sqrt{3 x (4) + 3 x (5 x)}}{\sqrt{3 x}}$

Factor $3 x$ out of $3 x (4) + 3 x (5 x)$ .

$\frac{\sqrt{3 x (4 + 5 x)}}{\sqrt{3 x}}$

Step 2

Combine $\sqrt{3 x (4 + 5 x)}$ and $\sqrt{3 x}$ into a single radical.

$\sqrt{\frac{3 x (4 + 5 x)}{3 x}}$

Step 3

Reduce the expression $\frac{3 x (4 + 5 x)}{3 x}$ by cancelling the common factors.

Cancel the common factor.

$\sqrt{\frac{3 x (4 + 5 x)}{3 x}}$

Rewrite the expression.

$\sqrt{\frac{x (4 + 5 x)}{x}}$

Step 4

Cancel the common factor of $x$ .

Cancel the common factor.

$\sqrt{\frac{x (4 + 5 x)}{x}}$

Divide $4 + 5 x$ by $1$ .

$\sqrt{4 + 5 x}$