Question

what is the product of $2\sqrt{5}$ and $10\sqrt{30}$ in simplest radical form?
answer attempt 1 out of 2

Explanation:

Step1: Multiply coefficients and radicals

$(2 \times 10) \times (\sqrt{5} \times \sqrt{30})$

Step2: Simplify coefficient and combine radicals

$20 \times \sqrt{5 \times 30} = 20\sqrt{150}$

Step3: Factor radical into perfect square

$20\sqrt{25 \times 6} = 20 \times \sqrt{25} \times \sqrt{6}$

Step4: Simplify perfect square radical

$20 \times 5 \times \sqrt{6} = 100\sqrt{6}$

Answer:

$100\sqrt{6}$