Question

current objective
use the product property to simplify square roots

question

simplify: \\(\sqrt{q^9}\\). assume that \\(q > 0\\).

provide your answer below:

Explanation:

Rewrite the radicand using the largest perfect square factor

$$ q^9 = q^8 \cdot q = (q^4)^2 \cdot q $$

Apply the product property of square roots

$$ \sqrt{q^9} = \sqrt{(q^4)^2 \cdot q} = \sqrt{(q^4)^2} \cdot \sqrt{q} $$

Simplify the perfect square term

$$ q^4\sqrt{q} $$

Answer:

Simplify: \(\sqrt{q^9}\). Assume that \(q > 0\).

Provide your answer below:
<blank>\(q^4\sqrt{q}\)</blank>