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cum arat ca radical din 11.025 este patrat perfect ?
dar radical din 32.400?
dau coroanaaa


Răspuns :

11.025 =10000+1000+25

=100²+2•100•5 +5²

=(100+5)²

=105²

32.400=40000 -2•200 •20 +400

=200²-2•200•20 +20²

=(200-20)^2

=180²


descompunem in factori primi

11025:5 2205 ; 2205:5 =441 ; 441:7 = 63 ; 63:7 = 9 ; 9 = 3x3 ;

11025 = 5²x7²x3² =(5x7x3)² = 105²= patrat perfect ;

32400:2 = 16200 ; 16200:2 = 8100 ; 8100:2 = 4050 ; 4050:2 = 2025 ;

2025:5 = 405 ; 405:5 = 81 ; 81:3 = 27 ; 27:3 = 9 ; 9 = 3x3 ;

32400 = 2⁴x5²x3⁴ = (2²x5x3²)² = (4x5x9)² = 180² = patrat perfect ;