Given a and b unit vectors, determine (2a-5b) . (b+3a)

if |a+b| =sqrt3

all a and b in the questions have a u-hat over top of them=unit vectors

can someone please check my work:

|a+b|=sqrt3

|a+b|^(0.5)=(a+b)(a+b)

3=2+2a.b

0.5=a.b

(2a-5b). (b+3a)

=-13a.b+6(a)^2-5(b)^2

=-13(0.5)+6(1)^2-5(1)^2

=-5.5

is my answer correct? mostly concerned about the a.b work