The 4th pattern A Major scale uses the E shape open chord. When looking at the open E chord, the root notes are on the open Top and Bottom E strings and the 2nd fret D string.
E
Important: The notes used in the A Major scale are A B C# D E F# G#, there are three sharps in the A 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“
| $1.4.$3.4.$4.4.$5.4.$6.4 | $1.X.$2.5.$5.5.$6.X | $3.6.$4.6 | $1.7.$2.7.$3.7.$4.X.$5.7.$6.7 |
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 5th fret A on the Bottom E string, and play up to the highest pitch note of the scale, 1st string 7th fret, which is a B note.
| $6.5 7 $5.4 5 7 $4.4 6 7 $3.4 6 7 $2.5 7 $1.4 5 7 |
Descending back to the lowest pitch note of the scale, the G# on the 4th fret Bottom E string.
| $1.7 5 4 $2.7 5 $3.7 6 4 $4.7 6 4 $5.7 5 4 $6.7 5 4 |
Then back up in pitch to the A root note on the 5th fret Bottom E string.
| $6.4 5 |