$  \sqrt{2} \simeq 1/4 \\ 3\sqrt{2} \simeq 4/2 \Rightarrow (3\sqrt{2}-4) \gt 0 \Rightarrow \sqrt[4]{(3\sqrt{2}-4)^4} = | 3\sqrt{2}-4 | = 3\sqrt{2}-4 \\ 2\sqrt{2} \simeq 2/8 \Rightarrow 5-2\sqrt{2} \gt 0 \Rightarrow \sqrt{(5-2\sqrt{2})^2} = | 5-2\sqrt{2} | = 5-2\sqrt{2} \\ (1-\sqrt{2})^2 = (1-\sqrt{2})(1-\sqrt{2}) = 1-\sqrt{2}-\sqrt{2}+2 = 3-2\sqrt{2} \\ H=(3\sqrt{2}-4)-(5-2\sqrt{2})+(3-2\sqrt{2}) = 3\sqrt{2}-6 $