Find the quantity if v=5i-7j and w=3i+2j, trig question!

Find the quantity if v=5i-7j and w=3i+2j
||v+w||

I dont know how to do this PLEASE HELP!!!
I already know the answer is, √89
I just need to know the steps to get with this answer

We wish to find the value of
||v+w||

if v=5i-7j and w=3i+2j
........_______
|r| =../r.+..r
.....√...1....2

if r = r(1)i +r(2)j

We first find the value of

v+ w by adding v(1) +w(1) = 5+3 = 8
and by adding v(2) +w(2) = -7+2 = -5

so v+w = 8i -5j

and
.............______
|v+w| = √8²+(-5)²
...._______
=√64 + 25
....___
=√89