16x\sqrt{\ 16x }

asked by guest
on Apr 09, 2025 at 10:31 pm



You asked:

Evaluate the expression: 16x\sqrt{16 x}

MathBot Answer:

Evaluated



16x=4x\displaystyle \sqrt{16 x} = 4 \sqrt{x}

Roots

16x=i256(re⁡(x))2+256(im⁡(x))24sin⁡(atan⁡2(16im⁡(x),16re⁡(x))2)+256(re⁡(x))2+256(im⁡(x))24cos⁡(atan⁡2(16im⁡(x),16re⁡(x))2)≈4.0i((re⁡(x))2+(im⁡(x))2)0.25sin⁡(atan⁡2(16im⁡(x),16re⁡(x))2)+4.0((re⁡(x))2+(im⁡(x))2)0.25cos⁡(atan⁡2(16im⁡(x),16re⁡(x))2)\sqrt{16 x} = i \sqrt[4]{256 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan}_{2}{\left(16 \operatorname{im}{\left(x\right)},16 \operatorname{re}{\left(x\right)} \right)}}{2} \right)} + \sqrt[4]{256 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan}_{2}{\left(16 \operatorname{im}{\left(x\right)},16 \operatorname{re}{\left(x\right)} \right)}}{2} \right)} \approx 4.0 i \left(\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(16 \operatorname{im}{\left(x\right)},16 \operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 4.0 \left(\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(16 \operatorname{im}{\left(x\right)},16 \operatorname{re}{\left(x\right)} \right)}}{2} \right)}16x=i(−256(re⁡(x))2+256(im⁡(x))24sin⁡(atan⁡2(16im⁡(x),16re⁡(x))2))−256(re⁡(x))2+256(im⁡(x))24cos⁡(atan⁡2(16im⁡(x),16re⁡(x))2)≈−4.0i((re⁡(x))2+(im⁡(x))2)0.25sin⁡(atan⁡2(16im⁡(x),16re⁡(x))2)−4.0((re⁡(x))2+(im⁡(x))2)0.25cos⁡(atan⁡2(16im⁡(x),16re⁡(x))2)\sqrt{16 x} = i \left(- \sqrt[4]{256 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan}_{2}{\left(16 \operatorname{im}{\left(x\right)},16 \operatorname{re}{\left(x\right)} \right)}}{2} \right)}\right) - \sqrt[4]{256 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan}_{2}{\left(16 \operatorname{im}{\left(x\right)},16 \operatorname{re}{\left(x\right)} \right)}}{2} \right)} \approx - 4.0 i \left(\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(16 \operatorname{im}{\left(x\right)},16 \operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 4.0 \left(\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(16 \operatorname{im}{\left(x\right)},16 \operatorname{re}{\left(x\right)} \right)}}{2} \right)}

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