Question

what is the product of $9\sqrt{3}$ and $5\sqrt{21}$ in simplest radical form?

Explanation:

Step1: Multiply coefficients and radicals

$(9 \times 5) \times (\sqrt{3} \times \sqrt{21})$

Step2: Calculate coefficient product, combine radicals

$45 \times \sqrt{3 \times 21} = 45\sqrt{63}$

Step3: Simplify the radical

$45\sqrt{9 \times 7} = 45 \times \sqrt{9} \times \sqrt{7} = 45 \times 3 \times \sqrt{7}$

Step4: Final coefficient calculation

$135\sqrt{7}$

Answer:

$135\sqrt{7}$