Upside Down Calculator Math Puzzle

Glen has a calculator which displays a maximum of seven digits. It is one of those calculators where each digit is represented by some combination of seven line segments. As Glen was playing with displaying numbers, he displayed a positive integer and his daughter, Suzie, turned it upside down and said, "Hey, I see a number that is a perfect square and I don't see any leading zeros.

Next Glen multiplied the number by 2. Suzie turned it upside down and said, "I see another number and it’s also a perfect square."

All the digits on Glen's calculator appear as digits when turned upside down except 3, 4, and 7.

What number did Glen originally display?

Thank you Susan Denham, in New Scientist

Click to find the answer to this math puzzle.