Simplify square root of x^2-2x+1

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

Step 1

Factor using the perfect square rule.

Rewrite $1$ as $1^{2}$ .

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

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 x = 2 \cdot x \cdot 1$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 1$ .

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

Step 2

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

$x - 1$