Simplify square root of 25(x+2)^4

$\sqrt{25 {(x + 2)}^{4}}$

Rewrite $25 {(x + 2)}^{4}$ as ${(5 {(x + 2)}^{2})}^{2}$ .

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

Pull terms out from under the radical, assuming positive real numbers.

$5 {(x + 2)}^{2}$

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

$5 ((x + 2) (x + 2))$

Expand $(x + 2) (x + 2)$ using the FOIL Method.

Apply the distributive property.

$5 (x (x + 2) + 2 (x + 2))$

Apply the distributive property.

$5 (x \cdot x + x \cdot 2 + 2 (x + 2))$

Apply the distributive property.

$5 (x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $2$ to the left of $x$ .

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

Multiply $2$ by $2$ .

$5 (x^{2} + 2 x + 2 x + 4)$

Add $2 x$ and $2 x$ .

$5 (x^{2} + 4 x + 4)$

Apply the distributive property.

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

Simplify.

Multiply $4$ by $5$ .

$5 x^{2} + 20 x + 5 \cdot 4$

Multiply $5$ by $4$ .

$5 x^{2} + 20 x + 20$