Question

rewrite the expression \\((\sqrt{8x^2})(\sqrt{10x^5})\\), where \\(x\\) is positive, without a perfect square factor in the radicand.

a. \\(80x^3\sqrt{5}\\)
b. \\(4x^7\sqrt{5}\\)
c. \\(4x^3\sqrt{5x}\\)
d. \\(4x^3\sqrt{5}\\)

Explanation:

Multiply the radicands

$$ (\sqrt{8x^2})(\sqrt{10x^5}) = \sqrt{8x^2 \cdot 10x^5} = \sqrt{80x^7} $$

Factor out perfect squares

$$ \sqrt{80x^7} = \sqrt{16 \cdot 5 \cdot x^6 \cdot x} = \sqrt{(16x^6) \cdot (5x)} $$

Simplify the radical

$$ \sqrt{16x^6} \cdot \sqrt{5x} = 4x^3\sqrt{5x} $$

Answer:

• A. \(80x^3\sqrt{5}\)
• B. \(4x^7\sqrt{5}\)
• C. \(4x^3\sqrt{5x}\) (Correct answer)
• D. \(4x^3\sqrt{5}\)