Simplify 5x^2 square root of 5x+3x square root of 5x^3

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

Step 1

Simplify each term.

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

Factor out $x^{2}$ .

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

Reorder $5$ and $x^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Step 2

Add $5 x^{2} \sqrt{5 x}$ and $3 x^{2} \sqrt{5 x}$ .

$8 x^{2} \sqrt{5 x}$