That's smaller than I expected. To convert that into human scale sqrt(500 million) = 22360, in millimeters that's around 22 meters (72 ft).
So if we had a square wall 22 meters by 22 meters we could paint a grid of 1 mm by 1 mm squares on it and end up with around 500 million squares.
Then we'd need to stand there in front of the wall with a laser pointer and shine the laser at each individual square and check the light bouncing back at us.
And there's uncertainty in whether your measurement is accurate.
And there's a background of other illuminated squares that can interfere with your readings.
And you're spinning while this is going on.
And the target square is continually moving. You might have just missed it.
1. Build a Dyson sphere around the sun.
2. Capture all the mass in the solar system to build a giant freaking laser.
3. Use the energy to from the Dyson sphere to power the laser.
4. Melt your entire civilization.
A very good laser has a beam divergence of tenths of milliradians, or 0.01 degrees. At the radius of planet 9, this is a very large beam, and we'd have a hard time putting out enough power to compete with the sun.
Furthermore, the sky has an area of 40,000 square degrees. Our little laser beam projects a circle with an area of 0.0000785 square degrees. You'd need to aim at 500 million spots to see the whole sky.