$\sqrt{x+2}$

asked by guest
on Nov 16, 2024 at 2:50 am



You asked:

Evaluate the expression: \(\sqrt{x + 2}\)

MathBot Answer:

Evaluated



\(\displaystyle \sqrt{x + 2} = \sqrt{x + 2} \)

Roots

\[\sqrt{x + 2} = i \sqrt[4]{\left(\operatorname{re}{\left(x\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} + 2 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(x\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} + 2 \right)}}{2} \right)} \approx 1.4142135623731 i \left(\left(0.5 \operatorname{re}{\left(x\right)} + 1\right)^{2} + 0.25 \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} + 2 \right)}}{2} \right)} + 1.4142135623731 \left(\left(0.5 \operatorname{re}{\left(x\right)} + 1\right)^{2} + 0.25 \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} + 2 \right)}}{2} \right)}\]\[\sqrt{x + 2} = i \left(- \sqrt[4]{\left(\operatorname{re}{\left(x\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} + 2 \right)}}{2} \right)}\right) - \sqrt[4]{\left(\operatorname{re}{\left(x\right)} + 2\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} + 2 \right)}}{2} \right)} \approx - 1.4142135623731 i \left(\left(0.5 \operatorname{re}{\left(x\right)} + 1\right)^{2} + 0.25 \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} + 2 \right)}}{2} \right)} - 1.4142135623731 \left(\left(0.5 \operatorname{re}{\left(x\right)} + 1\right)^{2} + 0.25 \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} + 2 \right)}}{2} \right)}\]

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