Simplify 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, assuming positive real numbers.

${(x - 1)}^{2}$

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 $x$ .

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

Move $- 1$ to the left of $x$ .

$x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1$

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x - 1 x - 1 \cdot - 1$

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x - x - 1 \cdot - 1$

Multiply $- 1$ by $- 1$ .

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

Subtract $x$ from $- x$ .

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