Question

use the product rule to simplify the radical.
$4\sqrt{125}$
$4\sqrt{125} = \square$
(simplify your answer. type an exact answer, using radicals as needed.)
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Explanation:

Step1: Factor radicand into perfect square

$125 = 25 \times 5$

Step2: Apply product rule for radicals

$4\sqrt{125} = 4\sqrt{25 \times 5} = 4 \times \sqrt{25} \times \sqrt{5}$

Step3: Simplify perfect square root

$\sqrt{25} = 5$, so $4 \times 5 \times \sqrt{5} = 20\sqrt{5}$

Answer:

$20\sqrt{5}$