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#