The coefficients and be added and/or subtracted - only if the radicands are the same. If they are not, there is no arithmetic, only simplification, if possible.
\(2\sqrt{50} + 5\sqrt{3}\)ex. a
What's the answer?
\(50 \longrightarrow 25 * 2 \longrightarrow (5 * 5) * 2 \longrightarrow 5^{1} * 5^{1} * 2^{1} \longrightarrow 5^{2} * 2^{1}\)
\(3 \longrightarrow 3^{1}\)
\(5^{2}\), noneThe highest perfect squares for each respective number are:
\(2\sqrt{50} + 5\sqrt{3} \longrightarrow 2\sqrt{5^{2} * 2^{1}} + 5\sqrt{3^{1}} \longrightarrow 2(5)\sqrt{2} + 5\sqrt{3} \longrightarrow 10\sqrt{2} + 5\sqrt{3} \)
Above is as much as it can be reduced because radicans cannot be made the same this time.
\(2\sqrt{75} - 4\sqrt{3}\)ex. b
\(75 \longrightarrow 25 * 3 \longrightarrow (5 * 5) * 3 \longrightarrow 5^{1} * 5^{1} * 3^{1} \longrightarrow 5^{2} * 3^{1}\)
\(3 \longrightarrow 3^{1}\)
\(5^{2}\), noneThe highest perfect squares for each respective number are:
\(2\sqrt{75} - 4\sqrt{3} \longrightarrow 2\sqrt{5^{2} * 3^{1}} - 4\sqrt{3^{1}} \longrightarrow 2(5)\sqrt{3} - 4\sqrt{3} \longrightarrow 10\sqrt{3} - 4\sqrt{3} \longrightarrow 6\sqrt{3} \)
The above problem had the same randicand, 3, so the coefficients of 10 and 4 were subtracted.
