解決1/2(1+sqrt{1+sqrt{2}})^-frac{1{2}}*(1+(1/2(1+sqrt{2})^-frac{1{2}}*(1+3/8sqrt{2}))) |Microsoft數學求解器

$$\frac { 1 } { 2 } ( 1 + \sqrt { 1 + \sqrt { 2 } } ) ^ { - \frac { 1 } { 2 } } \cdot ( 1 + ( \frac { 1 } { 2 } ( 1 + \sqrt { 2 } ) ^ { - \frac { 1 } { 2 } } \cdot ( 1 + \frac { 3 } { 8 \sqrt { 2 } } ) ) )$$

評估

$$\frac{\left(32\sqrt{\sqrt{2}+1}+3\sqrt{2}+16\right)\sqrt{\frac{\sqrt{2}-1}{\sqrt{\sqrt{2}+1}+1}}}{64}\approx 0.440262718$$

因式分解

$$\frac{\sqrt{\sqrt{2} - 1} {(32 \sqrt{\sqrt{2} + 1} + 3 \sqrt{2} + 16)}}{64 \sqrt{\sqrt{\sqrt{2} + 1} + 1}} = 0.44026271801722$$