Radicals are multiplied the same way as they're added or subtracted, the difference being the simplified radicands are multiplied after all the simplification etc. of them.
Again: The first step in simplification is taking a number (or numbers) which obviously isn't prime and breaking it down into a product of a prime or a product of primes and the largest perfect square.
\(5\sqrt{18} * 6\sqrt{12}\)What is the answer?
\(18:\,\,\,\,18 \div 4 = 4.5\,\,\,\,\,18 \div \underline{9} = 2 \,\,\,\, 18 \div 16 = 1.1\)
\(12:\,\,\,\,12 \div \underline{4} = 3 \,\,\,\, 12 \div 9 = 1.3 \)
\(so\)
\(5\sqrt{2 * 9} * 6\sqrt{3 * 4}\)
\(5\sqrt{2}(3) * 6\sqrt{3}(2)\)
\(15\sqrt{2} * 12\sqrt{3}\)
\(180\sqrt{6}\)
