Anyone know the shortcut to multiplying out (1+ rad(x))^8?

Question

I know there's a shortcut, but I don't want to look it up - I need to know this as a small part of a large calculus problem that I'm doing. And just in case you can't tell, the rad(x) is square root of x.

Answer 1

You need pascal's triangle and the binomial theorem.
use the 8th row of pascal's triangle (remember that the top (1) is the oth row) for the coefficents. you count down the exponents on the 1 and up on the exponents of rad x so that the exponents add up to 8.