Simplify the Radical Expression square root of (x+1)^4

$\sqrt{{(x + 1)}^{4}}$

Rewrite ${(x + 1)}^{4}$ as ${({(x + 1)}^{2})}^{2}$ .

$\sqrt{{({(x + 1)}^{2})}^{2}}$

Pull terms out from under the radical.

$| {(x + 1)}^{2} |$

Rewrite ${(x + 1)}^{2}$ as $(x + 1) (x + 1)$ .

$| (x + 1) (x + 1) |$

Expand $(x + 1) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$| x (x + 1) + 1 (x + 1) |$

Apply the distributive property.

$| x \cdot x + x \cdot 1 + 1 (x + 1) |$

Apply the distributive property.

$| x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1 |$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$| x^{2} + x \cdot 1 + 1 x + 1 \cdot 1 |$

Multiply $x$ by $1$ .

$| x^{2} + x + 1 x + 1 \cdot 1 |$

Multiply $x$ by $1$ .

$| x^{2} + x + x + 1 \cdot 1 |$

Multiply $1$ by $1$ .

$| x^{2} + x + x + 1 |$

Add $x$ and $x$ .

$| x^{2} + 2 x + 1 |$