$\sqrt{\30Box}$

asked by guest
on Oct 24, 2024 at 12:06 am



You asked:

Evaluate the expression: \(\sqrt{30 B o x}\)

MathBot Answer:

Evaluated



\(\displaystyle \sqrt{30 B o x} = \sqrt{30} \sqrt{B o x} \)

Roots

\[\sqrt{30 B o x} = i \sqrt[4]{900 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} + 900 \left(\operatorname{im}{\left(B o x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(30 \operatorname{im}{\left(B o x\right)},30 \operatorname{re}{\left(B o x\right)} \right)}}{2} \right)} + \sqrt[4]{900 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} + 900 \left(\operatorname{im}{\left(B o x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(30 \operatorname{im}{\left(B o x\right)},30 \operatorname{re}{\left(B o x\right)} \right)}}{2} \right)} \approx 5.47722557505166 i \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(30 \operatorname{im}{\left(B o x\right)},30 \operatorname{re}{\left(B o x\right)} \right)}}{2} \right)} + 5.47722557505166 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(30 \operatorname{im}{\left(B o x\right)},30 \operatorname{re}{\left(B o x\right)} \right)}}{2} \right)}\]\[\sqrt{30 B o x} = i \left(- \sqrt[4]{900 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} + 900 \left(\operatorname{im}{\left(B o x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(30 \operatorname{im}{\left(B o x\right)},30 \operatorname{re}{\left(B o x\right)} \right)}}{2} \right)}\right) - \sqrt[4]{900 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} + 900 \left(\operatorname{im}{\left(B o x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(30 \operatorname{im}{\left(B o x\right)},30 \operatorname{re}{\left(B o x\right)} \right)}}{2} \right)} \approx - 5.47722557505166 i \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(30 \operatorname{im}{\left(B o x\right)},30 \operatorname{re}{\left(B o x\right)} \right)}}{2} \right)} - 5.47722557505166 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(30 \operatorname{im}{\left(B o x\right)},30 \operatorname{re}{\left(B o x\right)} \right)}}{2} \right)}\]

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