The 3rd pattern G Major scale takes it’s root note positions from the G shape open chord. When looking at the open G chord, the root notes are on the open G string and the 3rd fret Top and Bottom E strings.
G
Important: The notes used in the G Major scale are G, A, B, C, D, E, F#, there is one sharp in the G Major scale.
If we take a look at the scale on the fretboard, you will see something like the following pattern… the root notes are marked with the “X“
| $1.0.$2.0.$3.X.$4.0.$5.0.$6.0 || $2.1 | $1.2.$3.2.$4.2.$5.2.$6.2 | $1.X.$2.3.$3.$5.3.$6.X | $4.4 |
Note: In the diagram above it’s the fret numbers that are indicated not the scale degrees, and it isn’t the way you would normally write out a scale using TAB, it’s just to illustrate the fingering pattern of the scale. 
When playing this scale on the guitar, I normally start on the lowest pitch root note, the 3rd fret Bottom E string with the ring finger, and play up to the highest pitch note of the scale, 1st string 3rd fret, which is also one of the G root notes.
| $6.3 $5.0 2 3 $4.0 2 4 $3.0 2 $2.0 1 3 $1.0 2 3 |
Descending back to the lowest pitch note of the scale, the E on the open bottom E string.
| $1.3 2 0 $2.3 1 0 $3.2 0 $4.4 2 0 $5.3 2 0 $6.3 2 0 |
Then back up in pitch to the G root note on the 3rd fret bottom E string.
| $6.0 2 3 |