new to calculus--test monday--limits

the limit as x approaches infinity of the square root of (4x^2 + 1)/8x + 7 equals....

This is what I have before I get lost...

1) I multiply by the conjugate to get 4x^2 + 1/8x+7 square root (4x^2 + 1)

2)then I multiply the numerator and denom by (1/x) to get (4x + 1/x) / 8 + 7/x square root (1/x^2 times (4x^2 + 1)

3) then I know that as x approaches infinity 1/x nears 0, 7/x nears 0, and square root of 1/x^2 nears 0, so I'm left wtih 4x/8? I have no clue!! help? what do I do when the numerator has a higher degree than the denom? any helpful hints in thinking this through?