Diagnosis
The router has an internal fan that usually only spins up under heavy load or high heat. If it's loud at idle, the fan curve in the firmware might be bugged, or the router is genuinely overheating.
How to Fix It
Log into the router's web interface (192.168.50.1). Go to Administration > System. Check the "Operating Mode". If it's set to "Media Streaming" or "Game Mode," these modes can ramp up the fan. Switch it back to "Wireless Router Mode" and see if the fan noise drops after a minute. Also, on that same page, you can manually adjust the fan setting between "Silent," "Performance," and "Auto." Try "Silent."
If That Didn't Work
Feel the top of the router. If it's very hot to the touch, it's overheating. Ensure it's standing upright with plenty of space above and below for airflow. Move it away from heat sources like a stereo amp or gaming console. Blow compressed air into the side vents to clear any dust clogging the heatsinks inside.
Heads Up
In some early firmware versions, there was a bug causing the fan to run at full speed unnecessarily. Updating to the latest firmware from the ASUS website often resolves it.