How do you simplify #sqrt(-225x^8)#?

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Answer 1 · 2015-05-22T13:43:17

By exponential rules, we know that #a^(n/m)=root(m)(a^n)#

Thus,

#sqrt(-225x^8)=root(2)(-225^1*x^8)=(-225^(1/2))(x^(8/2))=x^4sqrt(-(15^(2)))#

On the Real number's domain, this would be your final answer.

Considering imaginary numbers,

we have that #i^2=-1# and, thus, #sqrt(-1)=i#

#x^4sqrt((-1)(15^2))=x^4sqrt(-1)sqrt(15^2)=color(green)(15ix^4)#