We could solve this by factoring:
#2025#
#color(white)("XXXXX")##=5xx405#
#color(white)("XXXXX")##=5xx5xx81#
(maybe at this point we recognize #81=9^2#, but let's continue pretending we don't)
#color(white)("XXXXX")##=5xx5xx3xx27#
#color(white)("XXXXX")##=5xx5xx3xx3xx9#
#color(white)("XXXXX")##=5xx5xx3xx3xx3xx3#
and we have completely factored the given value.
Group the factoring in pairs of equal value:
#color(white)("XXXXX")##= color(red)(5xx5) xx color(green)(3xx3) xx color(blue)(3xx3)#
#color(white)("XXXXX")##= color(red)(5^2)xxcolor(green)(3^2)xxcolor(blue)(3^2)#
#color(white)("XXXXX")##= (color(red)(5)*color(green)(3)*color(blue)(3))^2#
#color(white)("XXXXX")##=45^2#
If #2025 = 45^2#
then
#color(white)("XXXXX")##sqrt(2025) = 45#
