Question

aratati ca numarul a=5^2 x 5^4 x 5^6 x ............. 5^100 este patrat perfect

Answer 1

$\displaystyle\it\\\boxed{\it a^a\cdot a^b \cdot a^c \cdot ... \cdot a^z =a^{a+b+c+...+z}}.\\------------------\\a=5^2\cdot5^4\cdot5^6\cdot...\cdot5^{100}=5^{2+4+6+...+100}=5^{2(1+2+3+...+50)}=\\(5^{1+2+3+...+50})^2 = patrat~perfect.$