S can only be 1,4,9,6,5 since it is the last digit of a square and not a leading zero.  But it is further restricted as being <4 since multiplying by 3 does not result in a carry.

Thus S=1

M is in {3,4,5} since 3*1xxxx = Mxxxx

The only 3 digit squares that end in 1 are: 121, 361, 441, 841, 961

but we can eliminate 121 and 441 since HIS has no repeat digits.

H is in {3,4,8,9}

I is in {4,6}

M is in {3,4,5}

At this point, I went with a program:

program output:

 MAJOR SIGHT 

 50382 16794

 HIS √HIS 

 961 31.0