$\sqrt{ $\sqrt{\44/5/4Box}$ }$

asked by guest
on Nov 16, 2024 at 7:48 am



You asked:

Evaluate the expression: 4454Box\sqrt{\sqrt{\frac{\frac{44}{5}}{4 B o x}}}

MathBot Answer:

Evaluated



4454Box=114⋅5341Box45\displaystyle \sqrt{\sqrt{\frac{\frac{44}{5}}{4 B o x}}} = \frac{\sqrt[4]{11} \cdot 5^{\frac{3}{4}} \sqrt[4]{\frac{1}{B o x}}}{5}

Roots

4454Box=i(−114⋅534im⁡(eiatan2⁡(−11im⁡(Box)5((re⁡(Box))2+(im⁡(Box))2),11re⁡(Box)5((re⁡(Box))2+(im⁡(Box))2))2(re⁡(Box))4+2(re⁡(Box))2(im⁡(Box))2+(im⁡(Box))44(re⁡(Box))2+(im⁡(Box))28)5)−114⋅534re⁡(eiatan2⁡(−11im⁡(Box)5((re⁡(Box))2+(im⁡(Box))2),11re⁡(Box)5((re⁡(Box))2+(im⁡(Box))2))2(re⁡(Box))4+2(re⁡(Box))2(im⁡(Box))2+(im⁡(Box))44(re⁡(Box))2+(im⁡(Box))28)5≈−1.21788328563091re⁡(eiatan2⁡(−11im⁡(Box)5((re⁡(Box))2+(im⁡(Box))2),11re⁡(Box)5((re⁡(Box))2+(im⁡(Box))2))2(re⁡(Box))4+2(re⁡(Box))2(im⁡(Box))2+(im⁡(Box))44(re⁡(Box))2+(im⁡(Box))28)−1.21788328563091iim⁡(eiatan2⁡(−11im⁡(Box)5((re⁡(Box))2+(im⁡(Box))2),11re⁡(Box)5((re⁡(Box))2+(im⁡(Box))2))2(re⁡(Box))4+2(re⁡(Box))2(im⁡(Box))2+(im⁡(Box))44(re⁡(Box))2+(im⁡(Box))28)\sqrt{\sqrt{\frac{\frac{44}{5}}{4 B o x}}} = i \left(- \frac{\sqrt[4]{11} \cdot 5^{\frac{3}{4}} \operatorname{im}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)}}{5}\right) - \frac{\sqrt[4]{11} \cdot 5^{\frac{3}{4}} \operatorname{re}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)}}{5} \approx - 1.21788328563091 \operatorname{re}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)} - 1.21788328563091 i \operatorname{im}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)}4454Box=i114⋅534im⁡(eiatan2⁡(−11im⁡(Box)5((re⁡(Box))2+(im⁡(Box))2),11re⁡(Box)5((re⁡(Box))2+(im⁡(Box))2))2(re⁡(Box))4+2(re⁡(Box))2(im⁡(Box))2+(im⁡(Box))44(re⁡(Box))2+(im⁡(Box))28)5+114⋅534re⁡(eiatan2⁡(−11im⁡(Box)5((re⁡(Box))2+(im⁡(Box))2),11re⁡(Box)5((re⁡(Box))2+(im⁡(Box))2))2(re⁡(Box))4+2(re⁡(Box))2(im⁡(Box))2+(im⁡(Box))44(re⁡(Box))2+(im⁡(Box))28)5≈1.21788328563091re⁡(eiatan2⁡(−11im⁡(Box)5((re⁡(Box))2+(im⁡(Box))2),11re⁡(Box)5((re⁡(Box))2+(im⁡(Box))2))2(re⁡(Box))4+2(re⁡(Box))2(im⁡(Box))2+(im⁡(Box))44(re⁡(Box))2+(im⁡(Box))28)+1.21788328563091iim⁡(eiatan2⁡(−11im⁡(Box)5((re⁡(Box))2+(im⁡(Box))2),11re⁡(Box)5((re⁡(Box))2+(im⁡(Box))2))2(re⁡(Box))4+2(re⁡(Box))2(im⁡(Box))2+(im⁡(Box))44(re⁡(Box))2+(im⁡(Box))28)\sqrt{\sqrt{\frac{\frac{44}{5}}{4 B o x}}} = i \frac{\sqrt[4]{11} \cdot 5^{\frac{3}{4}} \operatorname{im}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)}}{5} + \frac{\sqrt[4]{11} \cdot 5^{\frac{3}{4}} \operatorname{re}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)}}{5} \approx 1.21788328563091 \operatorname{re}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)} + 1.21788328563091 i \operatorname{im}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)}

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