Question

How is the process of adding and subtracting radicals similar to that of simplifying expressions with variables?

Answer 1

do you know the value of a radical?

Answer 2

the distributive property works regardless of what the known or unknown values are.

Answer 3

The two main operations you can perform when adding and subtracting radicals are:
simplifying radicals for example
\[√27=√3×9=√3*√9√= 3√3\]
and, once you have done this, gathering similar terms, for example \[√2+3√2=(1+3)√2 =4√2\]
Simplification is similar to the process in algebra of removing common factors from an expression, and gathering similar terms is very similar to gathering or combining terms in algebra.

Answer 4

the radical is treated exactly like a variable in a polynomial expression, following all of the same rules with one exception: if you square a radical it removes the radical over the term inside of it.

Answer 5

squaring a radical does not remove the radical ...

Answer 6

\[(\sqrt[3]{5})^2\ne5\]

Answer 7

ok, ok, technicality. If you square a square root, then it removes the radical.
If you cube a cube root, then it removes the radical.
Good catch, I wouldn't want someone following that to the letter not understanding what I intended to say.
@amistre64