You could do that, sure, but Memtest is theoretically the fastest way (even though it may seem like it takes the longest). Not only is it the 'fastest' way, but it's also the most efficient. It's the absolute best way to be sure whether or not your memory is healthy. The reason for this is it was programmed in mind to stress memory in various ways and on different levels. Each test represents a different part of the memory being stressed, etc. Also, Memtest is its own environment, it's entirely separate from the Operating System. Because of this, there's no way that any conflicts can occur and cause false positives. The only false positives that can occur are improper DRAM timings, voltages, etc, within the BIOS. If your memory is set to Auto, this should not be a problem. This is only a problem when the RAM is set to Manual or XMP (it may not be stable at those settings, and Auto is recommended for troubleshooting).
Regards,
Patrick