Explain how the process of combining radicals through addition and subtraction is similar to combining polynomials. What makes two radicals like radicals? Give an example.

Question

dumbcow · Answer

with like terms in polynomials
$$4x +2x = 6x$$
add coefficients
with radicals, treat them like a variable, add coefficients
$$4\sqrt{2} + 2\sqrt{2} = 6\sqrt{2}$$
as long as the inside of each radical is exactly the same

anonymous · Answer

ok take an example 
3x + 5 y + x = 4x + 5y
similarly
3sqrt + 5sqrt6 + sqrt3 = 4sqrt3 + 5sqrt6

(x + 2(x+3) = x^2 + 2x + 3x + 6 = x^2 +5x + 6
(2 + sqrt3)(3 + sqrt3) = 6 + 3sqrt3 + 2sqrt3 + 3
= 9 + 5sqrt3

anonymous · Answer

treat the radical like you treat the variable x