Question

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.

Answer 1

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

Answer 2

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

Answer 3

treat the radical like you treat the variable x