Ratios by ShapiroA

Question 8

A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.

This is a classical definition of what is now commonly known as the golden ratio. Mathematically, this ratio is Φ:1, where Φ ≈ 1.61803 to five decimal places. Give the square of Φ to five decimal places. (No calculators!)