143.64m2\sqrt{143.64m^{2}}

asked by guest
on Mar 28, 2025 at 4:38 pm



You asked:

Evaluate the expression: 143.64m2\sqrt{143.64 {m}^{2}}

MathBot Answer:

Evaluated



143.64m2=3399m25\displaystyle \sqrt{143.64 {m}^{2}} = \frac{3 \sqrt{399} \sqrt{m^{2}}}{5}

Expanded

143.64m2=3399m25\sqrt{143.64 {m}^{2}} = \frac{3 \sqrt{399} \sqrt{m^{2}}}{5}

Roots

143.64m2=i(3591(re⁡(m))225−3591(im⁡(m))225)2+51581124(re⁡(m))2(im⁡(m))26254sin⁡(atan2⁡(7182re⁡(m)im⁡(m)25,3591(re⁡(m))225−3591(im⁡(m))225)2)+(3591(re⁡(m))225−3591(im⁡(m))225)2+51581124(re⁡(m))2(im⁡(m))26254cos⁡(atan2⁡(7182re⁡(m)im⁡(m)25,3591(re⁡(m))225−3591(im⁡(m))225)2)≈16.9493362701906i(0.25((re⁡(m))2−(im⁡(m))2)2+(re⁡(m))2(im⁡(m))2)0.25sin⁡(atan2⁡(7182re⁡(m)im⁡(m)25,3591(re⁡(m))225−3591(im⁡(m))225)2)+16.9493362701906(0.25((re⁡(m))2−(im⁡(m))2)2+(re⁡(m))2(im⁡(m))2)0.25cos⁡(atan2⁡(7182re⁡(m)im⁡(m)25,3591(re⁡(m))225−3591(im⁡(m))225)2)\sqrt{143.64 {m}^{2}} = i \sqrt[4]{\left(\frac{3591 \left(\operatorname{re}{\left(m\right)}\right)^{2}}{25} - \frac{3591 \left(\operatorname{im}{\left(m\right)}\right)^{2}}{25}\right)^{2} + \frac{51581124 \left(\operatorname{re}{\left(m\right)}\right)^{2} \left(\operatorname{im}{\left(m\right)}\right)^{2}}{625}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{7182 \operatorname{re}{\left(m\right)} \operatorname{im}{\left(m\right)}}{25},\frac{3591 \left(\operatorname{re}{\left(m\right)}\right)^{2}}{25} - \frac{3591 \left(\operatorname{im}{\left(m\right)}\right)^{2}}{25} \right)}}{2} \right)} + \sqrt[4]{\left(\frac{3591 \left(\operatorname{re}{\left(m\right)}\right)^{2}}{25} - \frac{3591 \left(\operatorname{im}{\left(m\right)}\right)^{2}}{25}\right)^{2} + \frac{51581124 \left(\operatorname{re}{\left(m\right)}\right)^{2} \left(\operatorname{im}{\left(m\right)}\right)^{2}}{625}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{7182 \operatorname{re}{\left(m\right)} \operatorname{im}{\left(m\right)}}{25},\frac{3591 \left(\operatorname{re}{\left(m\right)}\right)^{2}}{25} - \frac{3591 \left(\operatorname{im}{\left(m\right)}\right)^{2}}{25} \right)}}{2} \right)} \approx 16.9493362701906 i \left(0.25 \left(\left(\operatorname{re}{\left(m\right)}\right)^{2} - \left(\operatorname{im}{\left(m\right)}\right)^{2}\right)^{2} + \left(\operatorname{re}{\left(m\right)}\right)^{2} \left(\operatorname{im}{\left(m\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{7182 \operatorname{re}{\left(m\right)} \operatorname{im}{\left(m\right)}}{25},\frac{3591 \left(\operatorname{re}{\left(m\right)}\right)^{2}}{25} - \frac{3591 \left(\operatorname{im}{\left(m\right)}\right)^{2}}{25} \right)}}{2} \right)} + 16.9493362701906 \left(0.25 \left(\left(\operatorname{re}{\left(m\right)}\right)^{2} - \left(\operatorname{im}{\left(m\right)}\right)^{2}\right)^{2} + \left(\operatorname{re}{\left(m\right)}\right)^{2} \left(\operatorname{im}{\left(m\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{7182 \operatorname{re}{\left(m\right)} \operatorname{im}{\left(m\right)}}{25},\frac{3591 \left(\operatorname{re}{\left(m\right)}\right)^{2}}{25} - \frac{3591 \left(\operatorname{im}{\left(m\right)}\right)^{2}}{25} \right)}}{2} \right)}143.64m2=i(−(3591(re⁡(m))225−3591(im⁡(m))225)2+51581124(re⁡(m))2(im⁡(m))26254sin⁡(atan2⁡(7182re⁡(m)im⁡(m)25,3591(re⁡(m))225−3591(im⁡(m))225)2))−(3591(re⁡(m))225−3591(im⁡(m))225)2+51581124(re⁡(m))2(im⁡(m))26254cos⁡(atan2⁡(7182re⁡(m)im⁡(m)25,3591(re⁡(m))225−3591(im⁡(m))225)2)≈−16.9493362701906i(0.25((re⁡(m))2−(im⁡(m))2)2+(re⁡(m))2(im⁡(m))2)0.25sin⁡(atan2⁡(7182re⁡(m)im⁡(m)25,3591(re⁡(m))225−3591(im⁡(m))225)2)−16.9493362701906(0.25((re⁡(m))2−(im⁡(m))2)2+(re⁡(m))2(im⁡(m))2)0.25cos⁡(atan2⁡(7182re⁡(m)im⁡(m)25,3591(re⁡(m))225−3591(im⁡(m))225)2)\sqrt{143.64 {m}^{2}} = i \left(- \sqrt[4]{\left(\frac{3591 \left(\operatorname{re}{\left(m\right)}\right)^{2}}{25} - \frac{3591 \left(\operatorname{im}{\left(m\right)}\right)^{2}}{25}\right)^{2} + \frac{51581124 \left(\operatorname{re}{\left(m\right)}\right)^{2} \left(\operatorname{im}{\left(m\right)}\right)^{2}}{625}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{7182 \operatorname{re}{\left(m\right)} \operatorname{im}{\left(m\right)}}{25},\frac{3591 \left(\operatorname{re}{\left(m\right)}\right)^{2}}{25} - \frac{3591 \left(\operatorname{im}{\left(m\right)}\right)^{2}}{25} \right)}}{2} \right)}\right) - \sqrt[4]{\left(\frac{3591 \left(\operatorname{re}{\left(m\right)}\right)^{2}}{25} - \frac{3591 \left(\operatorname{im}{\left(m\right)}\right)^{2}}{25}\right)^{2} + \frac{51581124 \left(\operatorname{re}{\left(m\right)}\right)^{2} \left(\operatorname{im}{\left(m\right)}\right)^{2}}{625}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{7182 \operatorname{re}{\left(m\right)} \operatorname{im}{\left(m\right)}}{25},\frac{3591 \left(\operatorname{re}{\left(m\right)}\right)^{2}}{25} - \frac{3591 \left(\operatorname{im}{\left(m\right)}\right)^{2}}{25} \right)}}{2} \right)} \approx - 16.9493362701906 i \left(0.25 \left(\left(\operatorname{re}{\left(m\right)}\right)^{2} - \left(\operatorname{im}{\left(m\right)}\right)^{2}\right)^{2} + \left(\operatorname{re}{\left(m\right)}\right)^{2} \left(\operatorname{im}{\left(m\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{7182 \operatorname{re}{\left(m\right)} \operatorname{im}{\left(m\right)}}{25},\frac{3591 \left(\operatorname{re}{\left(m\right)}\right)^{2}}{25} - \frac{3591 \left(\operatorname{im}{\left(m\right)}\right)^{2}}{25} \right)}}{2} \right)} - 16.9493362701906 \left(0.25 \left(\left(\operatorname{re}{\left(m\right)}\right)^{2} - \left(\operatorname{im}{\left(m\right)}\right)^{2}\right)^{2} + \left(\operatorname{re}{\left(m\right)}\right)^{2} \left(\operatorname{im}{\left(m\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{7182 \operatorname{re}{\left(m\right)} \operatorname{im}{\left(m\right)}}{25},\frac{3591 \left(\operatorname{re}{\left(m\right)}\right)^{2}}{25} - \frac{3591 \left(\operatorname{im}{\left(m\right)}\right)^{2}}{25} \right)}}{2} \right)}

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