Simplify square root of x^2+10x+25

$\sqrt{x^{2} + 10 x + 25}$

Step 1

Factor using the perfect square rule.

Rewrite $25$ as $5^{2}$ .

$\sqrt{x^{2} + 10 x + 5^{2}}$

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

$10 x = 2 \cdot x \cdot 5$

Rewrite the polynomial.

$\sqrt{x^{2} + 2 \cdot x \cdot 5 + 5^{2}}$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 5$ .

$\sqrt{{(x + 5)}^{2}}$

Step 2

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

$x + 5$