Question

write the following product in simplest form.
$2\sqrt{30} \cdot 3\sqrt{70}$
$2\sqrt{30} \cdot 3\sqrt{70} = \square$
(simplify your answer. type an exact answer, using radicals

Explanation:

Step1: Separate coefficients and radicals

$(2 \cdot 3) \cdot (\sqrt{30} \cdot \sqrt{70})$

Step2: Multiply coefficients and combine radicals

$6 \cdot \sqrt{30 \cdot 70}$

Step3: Simplify the product inside radical

$6 \cdot \sqrt{2100}$

Step4: Factor radical into perfect square

$6 \cdot \sqrt{100 \cdot 21}$

Step5: Simplify the perfect square radical

$6 \cdot 10\sqrt{21}$

Step6: Multiply remaining coefficients

$60\sqrt{21}$

Answer:

$60\sqrt{21}$