$\sqrt{20 $x^{2}$ }$

asked by guest
on Apr 10, 2025 at 2:03 am



You asked:

Evaluate the expression: 20x2\sqrt{20 {x}^{2}}

MathBot Answer:

Evaluated



20x2=25x2\displaystyle \sqrt{20 {x}^{2}} = 2 \sqrt{5} \sqrt{x^{2}}

Roots

20x2=i(20(re⁡(x))2−20(im⁡(x))2)2+1600(re⁡(x))2(im⁡(x))24sin⁡(atan⁡2(40re⁡(x)im⁡(x),20(re⁡(x))2−20(im⁡(x))2)2)+(20(re⁡(x))2−20(im⁡(x))2)2+1600(re⁡(x))2(im⁡(x))24cos⁡(atan⁡2(40re⁡(x)im⁡(x),20(re⁡(x))2−20(im⁡(x))2)2)≈6.32455532033676i(0.25((re⁡(x))2−(im⁡(x))2)2+(re⁡(x))2(im⁡(x))2)0.25sin⁡(atan⁡2(40re⁡(x)im⁡(x),20(re⁡(x))2−20(im⁡(x))2)2)+6.32455532033676(0.25((re⁡(x))2−(im⁡(x))2)2+(re⁡(x))2(im⁡(x))2)0.25cos⁡(atan⁡2(40re⁡(x)im⁡(x),20(re⁡(x))2−20(im⁡(x))2)2)\sqrt{20 {x}^{2}} = i \sqrt[4]{\left(20 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 20 \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + 1600 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan}_{2}{\left(40 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},20 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 20 \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(20 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 20 \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + 1600 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan}_{2}{\left(40 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},20 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 20 \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{2} \right)} \approx 6.32455532033676 i \left(0.25 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan}_{2}{\left(40 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},20 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 20 \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{2} \right)} + 6.32455532033676 \left(0.25 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan}_{2}{\left(40 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},20 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 20 \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{2} \right)}20x2=i(−(20(re⁡(x))2−20(im⁡(x))2)2+1600(re⁡(x))2(im⁡(x))24sin⁡(atan⁡2(40re⁡(x)im⁡(x),20(re⁡(x))2−20(im⁡(x))2)2))−(20(re⁡(x))2−20(im⁡(x))2)2+1600(re⁡(x))2(im⁡(x))24cos⁡(atan⁡2(40re⁡(x)im⁡(x),20(re⁡(x))2−20(im⁡(x))2)2)≈−6.32455532033676i(0.25((re⁡(x))2−(im⁡(x))2)2+(re⁡(x))2(im⁡(x))2)0.25sin⁡(atan⁡2(40re⁡(x)im⁡(x),20(re⁡(x))2−20(im⁡(x))2)2)−6.32455532033676(0.25((re⁡(x))2−(im⁡(x))2)2+(re⁡(x))2(im⁡(x))2)0.25cos⁡(atan⁡2(40re⁡(x)im⁡(x),20(re⁡(x))2−20(im⁡(x))2)2)\sqrt{20 {x}^{2}} = i \left(- \sqrt[4]{\left(20 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 20 \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + 1600 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan}_{2}{\left(40 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},20 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 20 \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{2} \right)}\right) - \sqrt[4]{\left(20 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 20 \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + 1600 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan}_{2}{\left(40 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},20 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 20 \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{2} \right)} \approx - 6.32455532033676 i \left(0.25 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan}_{2}{\left(40 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},20 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 20 \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{2} \right)} - 6.32455532033676 \left(0.25 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan}_{2}{\left(40 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},20 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 20 \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{2} \right)}

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