x= √3*0,(3)+√30*0.0(3)+ √300*0,00(3)+√3000* 0.000(3)
=
0,(3)=3/9=1/3
0.0(3)=3/90=1/30
0.00(3)=3/900=1/300
0.000(3)=3/9000=1/3000
= √3*1/3+√30*1/30+ √300*1/300+√3000*30000
=
=√1+√1+√1+√1=4 =2² deci patrat perfect
A= 3^2n*25^n+1-9^n+1* 5^2n=
=3^2n*5^2n+2-3^2n+2* 5^2n=
=3^2n*5^2n(5^2-3^2)=
=3^2n*5^2n×(25-9)=
=3^2n*5^2n×16=
=3*5^2n×4^2=
=(15^n×4)^2 deci patrat perfect
daca n impar 15^n×4=impar × impar × par =par
daca n impar 15^n×4=impar × par × par =par
pentru n=0 (15^n×4)^2 =(15^0×4)^2 =(1×4)^2=16 nu se divide cu 15
(3√49-2×√25):√121
=(3√7²-2*√5²):√11²
=(3×7-2×5):11
=(21-10):11
=11:11=1
(13√144-5√196)×√(√361-√225)=
(13×12-5×14)×√(19-15)=(156-70)×2=172
√(3⁴+ 3²* 2+1 * (2* √1296-3*√841)=
= √(3⁴+ 3²* 2+1* (2*36-3*29)=
= √(3⁴+ 3²* 2+1* (-15)=
= √(81+ 18+1)( -15)= √100 *(-15)=10*15=-150
