Simplify (x^2+6x+9)^(1/2)

${(x^{2} + 6 x + 9)}^{\frac{1}{2}}$

Step 1

Factor using the perfect square rule.

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

${(x^{2} + 6 x + 3^{2})}^{\frac{1}{2}}$

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.

${(x^{2} + 2 \cdot x \cdot 3 + 3^{2})}^{\frac{1}{2}}$

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

${({(x + 3)}^{2})}^{\frac{1}{2}}$

Step 2

Reduce the expression by cancelling the common factors.

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x + 3)}^{2 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x + 3)}^{2 (\frac{1}{2})}$

Rewrite the expression.

${(x + 3)}^{1}$

Step 3

Simplify.

$x + 3$