Simplify 2x^2 square root of 5x^4+7 square root of 5x^8

$2 x^{2} \sqrt{5 x^{4}} + 7 \sqrt{5 x^{8}}$

Simplify each term.

Rewrite $5 x^{4}$ as ${(x^{2})}^{2} \cdot 5$ .

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

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

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

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

Pull terms out from under the radical.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

$2 x^{4} \sqrt{5} + 7 \sqrt{5 x^{8}}$

Rewrite $5 x^{8}$ as ${({(x^{2})}^{2})}^{2} \cdot 5$ .

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

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

Reorder $5$ and ${(x^{4})}^{2}$ .

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

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

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

Pull terms out from under the radical.

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

Multiply the exponents in ${(x^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Multiply $2$ by $2$ .

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

$2 x^{4} \sqrt{5} + 7 x^{4} \sqrt{5}$

Add $2 x^{4} \sqrt{5}$ and $7 x^{4} \sqrt{5}$ .

$9 x^{4} \sqrt{5}$