Question

Demonstrati ca pentru orice numar natural n, numarul A=2^66n, este: a) patrat perfect; b) cub perfect

Answer 1

 

$\displaystyle \bf\\a)\\A=2^{66\times n}=2^{n\times 66}=2^{n\times33\times2}=\Big(2^{n\times33}\Big)^2 =\text{\bf patrat perfect}\\\\a)\\A=2^{66\times n}=2^{n\times 66}=2^{n\times22\times3}=\Big(2^{n\times22}\Big)^3 =\text{\bf cub perfect}$