Simplify square root of x^2-6x+9

$\sqrt{x^{2} - 6 x + 9}$

Step 1

Factor using the perfect square rule.

Rewrite $9$ as $3^{2}$ .

$\sqrt{x^{2} - 6 x + 3^{2}}$

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

$6 x = 2 \cdot x \cdot 3$

Rewrite the polynomial.

$\sqrt{x^{2} - 2 \cdot x \cdot 3 + 3^{2}}$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 3$ .

$\sqrt{{(x - 3)}^{2}}$

Step 2

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

$x - 3$