$\sqrt{\60x $x^{4}$ $y^{5}$}$

asked by guest
on Jan 15, 2025 at 3:28 am



You asked:

Evaluate the expression: \(\sqrt{60 x {x}^{4} {y}^{5}}\)

MathBot Answer:

Evaluated



\(\displaystyle \sqrt{60 x {x}^{4} {y}^{5}} = 2 \sqrt{15} \sqrt{x^{5} y^{5}} \)

Roots

\[\sqrt{60 x {x}^{4} {y}^{5}} = i \sqrt[4]{3600 \left(\operatorname{re}{\left(x^{5} y^{5}\right)}\right)^{2} + 3600 \left(\operatorname{im}{\left(x^{5} y^{5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(60 \operatorname{im}{\left(x^{5} y^{5}\right)},60 \operatorname{re}{\left(x^{5} y^{5}\right)} \right)}}{2} \right)} + \sqrt[4]{3600 \left(\operatorname{re}{\left(x^{5} y^{5}\right)}\right)^{2} + 3600 \left(\operatorname{im}{\left(x^{5} y^{5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(60 \operatorname{im}{\left(x^{5} y^{5}\right)},60 \operatorname{re}{\left(x^{5} y^{5}\right)} \right)}}{2} \right)} \approx 7.74596669241483 i \left(\left(\operatorname{re}{\left(x^{5} y^{5}\right)}\right)^{2} + \left(\operatorname{im}{\left(x^{5} y^{5}\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(60 \operatorname{im}{\left(x^{5} y^{5}\right)},60 \operatorname{re}{\left(x^{5} y^{5}\right)} \right)}}{2} \right)} + 7.74596669241483 \left(\left(\operatorname{re}{\left(x^{5} y^{5}\right)}\right)^{2} + \left(\operatorname{im}{\left(x^{5} y^{5}\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(60 \operatorname{im}{\left(x^{5} y^{5}\right)},60 \operatorname{re}{\left(x^{5} y^{5}\right)} \right)}}{2} \right)}\]\[\sqrt{60 x {x}^{4} {y}^{5}} = i \left(- \sqrt[4]{3600 \left(\operatorname{re}{\left(x^{5} y^{5}\right)}\right)^{2} + 3600 \left(\operatorname{im}{\left(x^{5} y^{5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(60 \operatorname{im}{\left(x^{5} y^{5}\right)},60 \operatorname{re}{\left(x^{5} y^{5}\right)} \right)}}{2} \right)}\right) - \sqrt[4]{3600 \left(\operatorname{re}{\left(x^{5} y^{5}\right)}\right)^{2} + 3600 \left(\operatorname{im}{\left(x^{5} y^{5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(60 \operatorname{im}{\left(x^{5} y^{5}\right)},60 \operatorname{re}{\left(x^{5} y^{5}\right)} \right)}}{2} \right)} \approx - 7.74596669241483 i \left(\left(\operatorname{re}{\left(x^{5} y^{5}\right)}\right)^{2} + \left(\operatorname{im}{\left(x^{5} y^{5}\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(60 \operatorname{im}{\left(x^{5} y^{5}\right)},60 \operatorname{re}{\left(x^{5} y^{5}\right)} \right)}}{2} \right)} - 7.74596669241483 \left(\left(\operatorname{re}{\left(x^{5} y^{5}\right)}\right)^{2} + \left(\operatorname{im}{\left(x^{5} y^{5}\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(60 \operatorname{im}{\left(x^{5} y^{5}\right)},60 \operatorname{re}{\left(x^{5} y^{5}\right)} \right)}}{2} \right)}\]

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