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Yes this will work well.
The Burris Eliminator III LaserScope 4-16x50mm Rifle Scope can handle that recoil of a 338 Magnum.
The Burris Eliminator III LaserScope 4-16x50mm Rifle Scope will have a hard time being used through thick brush.
The Burris Eliminator III LaserScope 4-16x50mm Rifle Scope has an integrated picatinny rail mount that would be used to mount to an AR platform. However, the Burris Eliminator III LaserScope 4-16x50mm Rifle Scope is currently not available.
The Burris Eliminator III LaserScope 4-16x50mm Rifle Scope has an integrated mount that mounts to picatinny rail or Weaver Base. You will need one to mount it to your rifle. Please email us at techsales@opticsplanet.com so we can help find a base for your rifle.
You will need a picatinny rail in order to mount the Burris Eliminator III LaserScope 4-16x50mm Rifle Scope to a rifle. Please email us at techsales@opticsplanet.com for more information.
The Burris Eliminator III LaserScope 4-16x50 mm Rifle Scope was not designed to be used with an Airgun as no ballistic calculations are provided/offered for airguns. I would recommend using a standard Airgun rated scope like the Hawke Sport Optics Airmax 3-9x40 AO Rifle Scope, which can be found by using the link below:
https://www.opticsplanet.com/hawke-sport-optics-airmax-3-9x40ao-riflescope.html
The Burris Eliminator III LaserScope 4-16x50 mm Rifle Scope has an integrated mount. This mount will directly attach the Burris Eliminator III LaserScope 4-16x50 mm Rifle Scope to a picatinny rail. You can view the mounting instructions on the left side of the product page.
The Burris Eliminator III LaserScope 4-16x50 mm Rifle Scope will not account for suppressors, it is multi caliber compatible for centerfire, rimfire, muzzleloader, and slug gun loads. It is not designed for precision shooting so it should still assist in providing a very close hold for your caliber.