Question

$\sqrt{1 \times 2 \times 3 \times 4 \times ......... \times 99 + 3}$
este nr irational?

Answer 1

$\displaystyle\sqrt{1*2*3*...*99+3} \\ \\ 1*2*3*...*99=10*1*2*3*...*99\implies U(1*2*3*...*99)=0 \\ \\ \implies U(1*2*3*...*99+3)=0+3=3 \\ \\ Ultima \ cifra \ a \ unui \ patrat \ perfect \ nu \ poate \ fi \ 3 \\ \\ \implies\sqrt{1*2*3*...*99+3}\in R \ fara \ Q$