Algebra Examples

$\sqrt{x^{2} - 12 x + 36}$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $36$ as $6^{2}$ .

$\sqrt{x^{2} - 12 x + 6^{2}}$

Step 1.2

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

$12 x = 2 \cdot x \cdot 6$

Step 1.3

Rewrite the polynomial.

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

Step 1.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 6$ .

$\sqrt{{(x - 6)}^{2}}$

Step 2

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

$x - 6$