Question

How do I go about simplifying this equation? (Using i = e="\sqrt{-1}" alt="\sqrt{-1}" align="absmiddle" class="latex-formula">)
$\sqrt{-3}\cdot \:2i\sqrt{8}\left(-2\right)\sqrt{-2}i^{88}$

Answer 1

Answer:

  16i√3

Step-by-step explanation:

I would write the radicals of negative numbers in terms of i, combine factors outside the radicals and combine factors inside the radicals. The power of i can be rewritten as a power of a power.

  $=i\sqrt{3}\cdot 2i\sqrt{8}(-2)i\sqrt{2}\cdot i^{88}\\\\=(2)(-2)\sqrt{(3)(8)(2)}\cdot i^{91}\\\\=-4\sqrt{48}\cdot (i^2)^{45}\cdot i\\\\=-16\sqrt{3}(-1)^{45}\cdot i\\\\=16i\sqrt{3}$