\sqrt(x-8)

asked by guest
on Nov 13, 2024 at 10:54 pm



You asked:

Evaluate the expression: \(\sqrt{x - 8}\)

MathBot Answer:

Evaluated



\(\displaystyle \sqrt{x - 8} = \sqrt{x - 8} \)

Roots

\[\sqrt{x - 8} = i \sqrt[4]{\left(\operatorname{re}{\left(x\right)} - 8\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} - 8 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(x\right)} - 8\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} - 8 \right)}}{2} \right)} \approx 2.82842712474619 i \left(\left(0.125 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 0.015625 \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} - 8 \right)}}{2} \right)} + 2.82842712474619 \left(\left(0.125 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 0.015625 \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} - 8 \right)}}{2} \right)}\]\[\sqrt{x - 8} = i \left(- \sqrt[4]{\left(\operatorname{re}{\left(x\right)} - 8\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} - 8 \right)}}{2} \right)}\right) - \sqrt[4]{\left(\operatorname{re}{\left(x\right)} - 8\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} - 8 \right)}}{2} \right)} \approx - 2.82842712474619 i \left(\left(0.125 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 0.015625 \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} - 8 \right)}}{2} \right)} - 2.82842712474619 \left(\left(0.125 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 0.015625 \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} - 8 \right)}}{2} \right)}\]

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