square root 8 plus square root minus square root of 32

asked by guest
on Nov 14, 2024 at 5:49 pm



You asked:

Evaluate the expression: 8+−32\sqrt{8 + \sqrt{-\sqrt{32}}}

MathBot Answer:

8+−32=8+2⋅24i\sqrt{8 + \sqrt{-\sqrt{32}}} = \sqrt{8 + 2 \cdot \sqrt[4]{2} i}

8+−32=8+−32=8+−4⋅2=8+−4⋅2=8+2⋅i⋅24\begin{aligned}\sqrt{8 + \sqrt{-\sqrt{32}}}&=\sqrt{8 + \sqrt{- \sqrt{32}}}\\&=\sqrt{8 + \sqrt{- 4 \cdot \sqrt{2}}}\\&=\sqrt{8 + \sqrt{-4 \cdot \sqrt{2}}}\\&=\sqrt{8 + 2 \cdot i \cdot \sqrt[4]{2}}\end{aligned}

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