Question

simplify. assume that no radicands were formed by raising negative quantities to even powers.

\\(\sqrt{28x^9}\\)

\\(\sqrt{28x^9} = \\)

(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression.)

Explanation:

Factor the radicand into perfect squares

$$ 28x^9 = (4 \cdot 7) \cdot (x^8 \cdot x) = (2^2 \cdot x^8) \cdot (7x) = (2x^4)^2 \cdot 7x $$

Apply the product rule for radicals

$$ \sqrt{28x^9} = \sqrt{(2x^4)^2 \cdot 7x} = \sqrt{(2x^4)^2} \cdot \sqrt{7x} $$

Simplify the perfect square term

$$ \sqrt{(2x^4)^2} \cdot \sqrt{7x} = 2x^4\sqrt{7x} $$

Answer:

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

\(\sqrt{28x^9} =\) <blank>\(2x^4\sqrt{7x}\)</blank>