Question

question

simplify: \\(\sqrt{72n^7}\\).

provide your answer below:

Explanation:

Factor the radicand into perfect squares

$$ 72n^7 = (36 \cdot 2) \cdot (n^6 \cdot n) = (36n^6) \cdot (2n) $$

Apply the product rule for radicals

$$ \sqrt{72n^7} = \sqrt{36n^6} \cdot \sqrt{2n} $$

Simplify the perfect square radical

$$ \sqrt{36n^6} \cdot \sqrt{2n} = 6n^3\sqrt{2n} $$

Answer:

\(6n^3\sqrt{2n}\)