Multiplying Radicals
Posted: Thu Jan 08, 2026 6:41 pm
You multiply the coefficients with each other - and then the radicands, after simplification, with each other.
\(5\sqrt{18} * 6\sqrt{12}\)What is the answer?
\(18 \longrightarrow 2 * 9 \longrightarrow 2 * 3 * 3 \longrightarrow 2^{1} * 3^{1} * 3^{1} \longrightarrow 2^{1} * 3^{2}\)
\(12 \longrightarrow 3 * 4 \longrightarrow 3 * 2 * 2 \longrightarrow 3^{1} * 2^{1} * 2^{1} \longrightarrow 3^{1} * 2^{2} \)
\(3^{2}, 2^{2}\)The highest perfect squares for each respective number are:
\(5\sqrt{18} * 6\sqrt{12} \longrightarrow 5\sqrt{2^{1} * 3^{2}} * 6\sqrt{3^{1} * 2^{2}} \longrightarrow 5(3)\sqrt{2} * 6(2)\sqrt{3} \longrightarrow 15\sqrt{2} * 12\sqrt{3} \longrightarrow 180\sqrt{6}\)