Show $(m^2+n^2)(o^2+p^2)(r^2+s^2) \geq 8mnoprs$ Let $m,n,o,p,r,s$ be positive numbers. Show that:
$$(m^2+n^2)(o^2+p^2)(r^2+s^2) \geq 8mnoprs$$
I tested an example,
let $m,n,o,p,r,s=1,2,3,4,5,6$ respectively. Then:
$$(1+4)(9+16)(25+30)=(5)(25)(55) \geq 8123456$$
but I get $6875$ which is not greater than the right side.
So am i misunderstanding the problem? Any ideas?

Yes, you misunderstood the problem, for $8mnoprs$ has tacit multiplication signs, it does not mean concatenation. Therefore, your test case is $$(1 + 4)(9 + 16)(25 + 30) = 6875 \geq 8 \times 1 \times 2 \times 3 \times 4 \times 5 \times 6.$$ But the first case I would test is the minimal case $m = n = o = p = r = s = 1$. Then $$2 \times 2 \times 2 \geq 8 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1.$$
