Am I able to purchase apple care for this device?

AppleCare is available for purchase for 60 days from the purchase date. If you are still within that time frame then you should be able to purchase from settings. See this article: Buy an AppleCare plan - Apple Support

acqueline43 Said:

"Am I able to purchase apple care for this device?: I would like to purchase apple care for this device. How do I go about doing that?"

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Verify if AppleCare is Available:

1. Get the Serial Number: Find the Serial Number or IMEI on your iPhone, iPad, or iPod touch - Apple Support
2. Enter it Here: checkcoverage.apple.com
3. Proceed form there.

I believe that you can buy AopleCare for a new iPhone or one from the Refurbished Store, at the time of purchase or within the warranty period.

[EDIT: Looks like I was wrong, and you usually have much less than a year from the purchase date.]

In the case of an iPhone 8, it probably would be too late to get AppleCare now.