Simplify 5x square root of 28x^5+8x^3 square root of 7x

$5 x \sqrt{28 x^{5}} + 8 x^{3} \sqrt{7 x}$

Simplify each term.

Rewrite $28 x^{5}$ as ${(2 x^{2})}^{2} \cdot (7 x)$ .

Factor $4$ out of $28$ .

$5 x \sqrt{4 (7) x^{5}} + 8 x^{3} \sqrt{7 x}$

Rewrite $4$ as $2^{2}$ .

$5 x \sqrt{2^{2} \cdot 7 x^{5}} + 8 x^{3} \sqrt{7 x}$

Factor out $x^{4}$ .

$5 x \sqrt{2^{2} \cdot 7 (x^{4} x)} + 8 x^{3} \sqrt{7 x}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$5 x \sqrt{2^{2} \cdot 7 ({(x^{2})}^{2} x)} + 8 x^{3} \sqrt{7 x}$

Move $7$ .

$5 x \sqrt{2^{2} {(x^{2})}^{2} \cdot 7 x} + 8 x^{3} \sqrt{7 x}$

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

$5 x \sqrt{{(2 x^{2})}^{2} \cdot 7 x} + 8 x^{3} \sqrt{7 x}$

Add parentheses.

$5 x \sqrt{{(2 x^{2})}^{2} \cdot (7 x)} + 8 x^{3} \sqrt{7 x}$

Pull terms out from under the radical.

$5 x (2 x^{2} \sqrt{7 x}) + 8 x^{3} \sqrt{7 x}$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$5 (x^{2} x) (2 \sqrt{7 x}) + 8 x^{3} \sqrt{7 x}$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$5 (x^{2} x^{1}) (2 \sqrt{7 x}) + 8 x^{3} \sqrt{7 x}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 x^{2 + 1} (2 \sqrt{7 x}) + 8 x^{3} \sqrt{7 x}$

Add $2$ and $1$ .

$5 x^{3} (2 \sqrt{7 x}) + 8 x^{3} \sqrt{7 x}$

Multiply $2$ by $5$ .

$10 x^{3} \sqrt{7 x} + 8 x^{3} \sqrt{7 x}$

Add $10 x^{3} \sqrt{7 x}$ and $8 x^{3} \sqrt{7 x}$ .

$18 x^{3} \sqrt{7 x}$