Simplify square root of x^2-18x+81

$\sqrt{x^{2} - 18 x + 81}$

Step 1

Factor using the perfect square rule.

Rewrite $81$ as $9^{2}$ .

$\sqrt{x^{2} - 18 x + 9^{2}}$

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

$18 x = 2 \cdot x \cdot 9$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 9$ .

$\sqrt{{(x - 9)}^{2}}$

Step 2

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

$x - 9$