Simplify 3 square root of 45x^3+ square root of 5x

$3 \sqrt{45 x^{3}} + \sqrt{5 x}$

Rewrite $45 x^{3}$ as ${(3 x)}^{2} \cdot (5 x)$ .

Factor $9$ out of $45$ .

$3 \sqrt{9 (5) x^{3}} + \sqrt{5 x}$

Rewrite $9$ as $3^{2}$ .

$3 \sqrt{3^{2} \cdot 5 x^{3}} + \sqrt{5 x}$

Factor out $x^{2}$ .

$3 \sqrt{3^{2} \cdot 5 (x^{2} x)} + \sqrt{5 x}$

Move $5$ .

$3 \sqrt{3^{2} x^{2} \cdot 5 x} + \sqrt{5 x}$

Rewrite $3^{2} x^{2}$ as ${(3 x)}^{2}$ .

$3 \sqrt{{(3 x)}^{2} \cdot 5 x} + \sqrt{5 x}$

Add parentheses.

$3 \sqrt{{(3 x)}^{2} \cdot (5 x)} + \sqrt{5 x}$

$3 \sqrt{{(3 x)}^{2} \cdot (5 x)} + \sqrt{5 x}$

Pull terms out from under the radical.

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

Multiply $3$ by $3$ .

$9 x \sqrt{5 x} + \sqrt{5 x}$

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