Question

to find the product of \\((-2\sqrt{20k})(5\sqrt{8k^3})\\), first write using a single radical. which expression is equivalent to the given product?

• \\(-10\sqrt{160k^3}\\)
• \\(-10\sqrt{160k^4}\\)
• \\(3\sqrt{28k^4}\\)
• \\(3\sqrt{28k^3}\\)

Explanation:

Multiply the coefficients outside the radicals

Using the Exponent Rules knowledge point

$$ -2 \cdot 5 = -10 $$

Multiply the expressions inside the radicals

Using the Product Property of Radicals knowledge point

$$ \sqrt{20k} \cdot \sqrt{8k^3} = \sqrt{20k \cdot 8k^3} = \sqrt{160k^4} $$

Combine the results into a single expression

Using the Product Property of Radicals knowledge point

$$ (-2\sqrt{20k})(5\sqrt{8k^3}) = -10\sqrt{160k^4} $$

Answer:

• (A) \(-10\sqrt{160k^3}\)
• (B) \(-10\sqrt{160k^4}\) (Correct answer)
• (C) \(3\sqrt{28k^4}\)
• (D) \(3\sqrt{28k^3}\)