In addition and subtraction of radicals, group the like terms or the radicals with the same index and radicand.
If the radicands are not the same, try simplifying the radicands by finding their factors in such a way that one of the factors has the root of the index.
Example:
[tex] \sqrt{20}, \sqrt{80} , \sqrt{5} [/tex]
are not like terms because they don't have the same radicands although they have the same index which is 2 (square root).
Factor the radicands:
[tex] \sqrt{20} = \sqrt{(4)(5)} = 2 \sqrt{5} [/tex]
[tex] \sqrt{80} = \sqrt{((16)(5)} = 4 \sqrt{5} [/tex]
[tex] \sqrt{5} = \sqrt{5} [/tex]
They radicals now have the same radicands; you may add or subtract its coefficient.
(Please check my handwritten solution, attached.)
