Simplify #sqrt("-"180 x^16)#
#"Write the expression as a set of factors that are perfect squares, as far as possible."#
1) Factoring #"-"180# into perfect squares as far as possible:
#color(white)(.........)##"-"180#
#color(white)(...)#╱ #color(white)(.)# ⧸ #color(white)(.)# ⧹ #color(white)(,)#╲
#("-"1) (2^2) (3^2) (5)#
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2) Factoring #x^16# into a perfect square
#color(white)(..)##(x^8)^2#
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3) Here's how it looks when it's all put together
#sqrt(("-"1)(5) (2^2) (3^2) (x^8)^2#
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4) Write the square roots of the perfect squares outside,
but leave the other factors as is
#+- 2*3*x^8sqrt(("-"1)(5)#
#+- 6 x^8sqrt(("-"1)(5)#
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5) Write #sqrt("-"1)# as #i#
#+- 6 x^8sqrt("-"1) sqrt(5)#
#+- 6 x^8 i sqrt(5) #
