解決01/3*(4*01*sqrt{1+01^3}+2*02sqrt{1+02^3}+4*03sqrt{1+03^3}+2*04sqrt{1+04^3}+4*05sqrt{1+{05}^{3}}+2*06sqrt{1+{06}^3}+4*07sqrt{1+{07}^3}+2*08sqrt{1+{08}^3}+4*09sqrt{1+{09}^3}+1+sqrt{2}) |Microsoft數學求解器

$$\frac{ 01 }{ 3 } \times (4 \times 01 \times \sqrt{ 1+ { 01 }^{ 3 } } +2 \times 02 \sqrt{ 1+ { 02 }^{ 3 } } +4 \times 03 \sqrt{ 1+ { 03 }^{ 3 } } +2 \times 04 \sqrt{ 1+ { 04 }^{ 3 } } +4 \times 05 \sqrt{ 1+ { 05 }^{ 3 } } +2 \times 06 \sqrt{ 1+ { 06 }^{ 3 } } +4 \times 07 \sqrt{ 1+ { 07 }^{ 3 } } +2 \times 08 \sqrt{ 1+ { 08 }^{ 3 } } +4 \times 09 \sqrt{ 1+ { 09 }^{ 3 } } +1+ \sqrt{ 2 } )$$

評估

$$0$$

解題步驟

將 0 乘上 1 得到 0。

$$\frac{0}{3}\left(0\times 1\times 4\sqrt{1+\left(0\times 1\right)^{3}}+0\times 2\times 2\sqrt{1+\left(0\times 2\right)^{3}}+0\times 3\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 2\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 4\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 2\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 4\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 2\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 4\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

零除以任何非零的數字結果都會是零。

$$0\left(0\times 1\times 4\sqrt{1+\left(0\times 1\right)^{3}}+0\times 2\times 2\sqrt{1+\left(0\times 2\right)^{3}}+0\times 3\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 2\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 4\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 2\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 4\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 2\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 4\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

完成乘法。

$$0\left(0\times 4\sqrt{1+\left(0\times 1\right)^{3}}+0\times 2\sqrt{1+\left(0\times 2\right)^{3}}+0\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 4 得到 0。

$$0\left(0\sqrt{1+\left(0\times 1\right)^{3}}+0\times 2\sqrt{1+\left(0\times 2\right)^{3}}+0\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 1 得到 0。

$$0\left(0\sqrt{1+0^{3}}+0\times 2\sqrt{1+\left(0\times 2\right)^{3}}+0\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 0 的 3 乘冪，然後得到 0。

$$0\left(0\sqrt{1+0}+0\times 2\sqrt{1+\left(0\times 2\right)^{3}}+0\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 1 與 0 相加可以得到 1。

$$0\left(0\sqrt{1}+0\times 2\sqrt{1+\left(0\times 2\right)^{3}}+0\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 1 的平方根，並得到 1。

$$0\left(0\times 1+0\times 2\sqrt{1+\left(0\times 2\right)^{3}}+0\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 1 得到 0。

$$0\left(0+0\times 2\sqrt{1+\left(0\times 2\right)^{3}}+0\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 2 得到 0。

$$0\left(0+0\sqrt{1+\left(0\times 2\right)^{3}}+0\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 2 得到 0。

$$0\left(0+0\sqrt{1+0^{3}}+0\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 0 的 3 乘冪，然後得到 0。

$$0\left(0+0\sqrt{1+0}+0\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 1 與 0 相加可以得到 1。

$$0\left(0+0\sqrt{1}+0\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 1 的平方根，並得到 1。

$$0\left(0+0\times 1+0\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 1 得到 0。

$$0\left(0+0+0\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 與 0 相加可以得到 0。

$$0\left(0\times 4\sqrt{1+\left(0\times 3\right)^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 4 得到 0。

$$0\left(0\sqrt{1+\left(0\times 3\right)^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 3 得到 0。

$$0\left(0\sqrt{1+0^{3}}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 0 的 3 乘冪，然後得到 0。

$$0\left(0\sqrt{1+0}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 1 與 0 相加可以得到 1。

$$0\left(0\sqrt{1}+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 1 的平方根，並得到 1。

$$0\left(0\times 1+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 1 得到 0。

$$0\left(0+0\times 4\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 4 得到 0。

$$0\left(0+0\sqrt{1+\left(0\times 4\right)^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 4 得到 0。

$$0\left(0+0\sqrt{1+0^{3}}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 0 的 3 乘冪，然後得到 0。

$$0\left(0+0\sqrt{1+0}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 1 與 0 相加可以得到 1。

$$0\left(0+0\sqrt{1}+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 1 的平方根，並得到 1。

$$0\left(0+0\times 1+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 1 得到 0。

$$0\left(0+0+0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 與 0 相加可以得到 0。

$$0\left(0\times 5\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 5 得到 0。

$$0\left(0\sqrt{1+\left(0\times 5\right)^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 5 得到 0。

$$0\left(0\sqrt{1+0^{3}}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 0 的 3 乘冪，然後得到 0。

$$0\left(0\sqrt{1+0}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 1 與 0 相加可以得到 1。

$$0\left(0\sqrt{1}+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 1 的平方根，並得到 1。

$$0\left(0\times 1+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 1 得到 0。

$$0\left(0+0\times 6\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 6 得到 0。

$$0\left(0+0\sqrt{1+\left(0\times 6\right)^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 6 得到 0。

$$0\left(0+0\sqrt{1+0^{3}}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 0 的 3 乘冪，然後得到 0。

$$0\left(0+0\sqrt{1+0}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 1 與 0 相加可以得到 1。

$$0\left(0+0\sqrt{1}+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 1 的平方根，並得到 1。

$$0\left(0+0\times 1+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 1 得到 0。

$$0\left(0+0+0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 與 0 相加可以得到 0。

$$0\left(0\times 7\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 7 得到 0。

$$0\left(0\sqrt{1+\left(0\times 7\right)^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 7 得到 0。

$$0\left(0\sqrt{1+0^{3}}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 0 的 3 乘冪，然後得到 0。

$$0\left(0\sqrt{1+0}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 1 與 0 相加可以得到 1。

$$0\left(0\sqrt{1}+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 1 的平方根，並得到 1。

$$0\left(0\times 1+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 1 得到 0。

$$0\left(0+0\times 8\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 8 得到 0。

$$0\left(0+0\sqrt{1+\left(0\times 8\right)^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 8 得到 0。

$$0\left(0+0\sqrt{1+0^{3}}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 0 的 3 乘冪，然後得到 0。

$$0\left(0+0\sqrt{1+0}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 1 與 0 相加可以得到 1。

$$0\left(0+0\sqrt{1}+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

計算 1 的平方根，並得到 1。

$$0\left(0+0\times 1+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 1 得到 0。

$$0\left(0+0+0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 與 0 相加可以得到 0。

$$0\left(0\times 9\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 9 得到 0。

$$0\left(0\sqrt{1+\left(0\times 9\right)^{3}}+1+\sqrt{2}\right)$$

將 0 乘上 9 得到 0。

$$0\left(0\sqrt{1+0^{3}}+1+\sqrt{2}\right)$$

計算 0 的 3 乘冪，然後得到 0。

$$0\left(0\sqrt{1+0}+1+\sqrt{2}\right)$$

將 1 與 0 相加可以得到 1。

$$0\left(0\sqrt{1}+1+\sqrt{2}\right)$$

計算 1 的平方根，並得到 1。

$$0\left(0\times 1+1+\sqrt{2}\right)$$

將 0 乘上 1 得到 0。

$$0\left(0+1+\sqrt{2}\right)$$

將 0 與 1 相加可以得到 1。

$$0\left(1+\sqrt{2}\right)$$

任何項目乘以零的結果都會是零。

$$0$$

因式分解

$$0$$