$\left(\sqrt{56+\sqrt{56+\sqrt{56+\cdots \infty }}}\right)\left(\sqrt{56-\sqrt{56-\sqrt{56-\cdots \infty }}}\right)=$

$\text{Let }x=\sqrt{56+\sqrt{56+\sqrt{56+\cdots \infty Y^{ }}}}$

$x=\sqrt{56+x}$

$x^2=56+x$

$x^2-x+56=0$

$x=8,x=-7\left(\text{neglected}\right)$

$\text{Let }y=\sqrt{56-\sqrt{56-\sqrt{56-\cdots \infty }}}$

$y=\sqrt{56-y}$

$y^2=56-y$

$y^2+y-56=0\Rightarrow y^2+8y-7y-56=0$

$y=-8\left(\text{neglected}\right)y=7$

$x\times y=7\times 8=56$