(1)
The square root of 8 is somewhere between 2 and 3, because
[tex]2^2=4<8,\quad 3^2=9>8[/tex]
So, [tex]\sqrt{8}-2[/tex] is between -1 and 0, whereas [tex]5-\sqrt{8}[/tex] is between 2 and 3.
So, we have
[tex]\sqrt{8}-2<5-\sqrt{8}[/tex]
(2)
The square root of 25 is 5, because [tex]5^2=25[/tex]
So, the left hand side is exactly
[tex]\sqrt{25}-2=5-2=3[/tex]
You seem to have already computed the right hand side to be 2.30, so we have
[tex]\sqrt{25}-2>2.30[/tex]
