First of all, we would certainly recommend hardwiring the whole house with Ethernet cables as this will minimize your radiation exposure. Wifi is two-way traffic and your iPad, smart phone and other wireless devices still emit the same amount of radiation.
How many router you would need really depends on the building materials. For example, reinforced concrete walls and ceilings attenuate the wifi signal strongly while the signal will pass through wood virtually unattenuated.
The best advice is to place a number of Eco-wifi routers in enough locations in your house to provide optimal coverage, and hardwire the LAN connections from your Internet modem to each of them. Alternatively you may daisy-chain them by pulling a wire from one Eco-wifi router to another.
If you have existing coaxial TV cabling in your house the Hischmann MA-32 network adapters may be a good solution so that you don’t need to pull LAN cables. The way these work is that you place a 2nd Eco-wifi router in the room where you want to have additional wifi coverage, then connect that router to the Hirschmann MA32 adapter, and connect the Hirschmann MA32 to the TV coax outlet available in that room. Then you connect your Internet modem to the 2nd Hirschmann MA32 adapter, and connect that Hirschmann MA32 to the TV coax cable/outlet near the Internet modem. In this way the coax connection replaces the Ethernet LAN cable you would otherwise need to pull from the Internet modem to the 2nd Eco-wifi router.
Another solution exists, powerline adapters, but they work with a signal at a frequency of around 30 Megahertz that is fed into the power lines. These act as a kind of antenna because they are not shielded, and radiate the signal around your house. Sometimes neighboring amateur broadcasters even complain about the interference of the powerline adapters. This option is therefore not completely radiation-free and it is much better to pull LAN cables.
It may be tempting to use a wifi mesh router system, but do understand that these are dramatic in terms of wifi radiation exposure. All wireless signals are transmitted double, triple, quadruple from one mesh node to another.