If the number is X then, reading it through . . .
when she multiples it by itself is 'squared', she then adds 10.01 and get 91.01
The equations is: x^2 + 10.01 = 91.01
Solving: x^2 = 91.01 - 10.01
x^2 = 81
x = +9 or -9 as both +9 and -9 squared = 81
