Binomial Theorem for fractional exponents..

I have a question that says:
write out the general binomial expansion of (1+x)^n up to and including third order terms. Use the expression to show that √5 ≈ 1145/512
HINT: 5=4+1
I really don't know how to solve this, I know that I should put it in the form of (1+x)^1/2 but how?
After I do that can I just substitute normally in the binomial expansion???
I would really appreciate any help I can get!
Thanks!

The binomial series converges for |x| < 1.
So, we need to rewrite √5 a little bit.

Note that
√5 = √(4 + 1)
.....= √(4(1 + 1/4))
.....= 2 * (1 + 1/4)^(1/2).

Now, x = 1/4, which has absolute value < 1.

So, √5 = 2 * (1 + 1/4)^(1/2).
...........≈ 2 [1 + (1/2)x + [(1/2)(1/2 - 1)/2!] x^2 + [(1/2)(1/2 - 1)(1/2 - 2)/3!] x^3] {at x = 1/4}
...........= 2 + x - (1/4) x^2 + (1/8) x^3 {at x = 1/4}
...........= 2 + 1/4 - (1/4) (1/4)^2 + (1/8) (1/4)^3
...........= 1145/512 ≈ 2.236.

I hope this helps!