In order to do arithmetic on radicals, simplification, if possible, must be done first.
And simplifying radicals is about breaking down the radicands into products, then expressing them as powers - then multiplying them - after which looking for a highest perfect square.
And the square root of the perfect square is taken - and so this number is placed to the outside of the radicand. It is multiplied to the coefficient, if there is one.
\(5\sqrt{44}\)What is the following radical when simplified?
\(44 \longrightarrow 4 * 11 \longrightarrow (2 * 2) * 11 \longrightarrow 2^{1} * 2^{1} * 11^{1} \longrightarrow 2^{2} * 11^{1}\)
\(2^{2}\)The highest perfect square is:
\(5\sqrt{44} \longrightarrow 5\sqrt{2^{2} * 11^{1}} \longrightarrow 5(2)\sqrt{11} \longrightarrow 10\sqrt{11} \)
