How do you simplify #-9^(1/2)#?

2 Answers
Acquaintance
Jun 30, 2016

#3i#

Explanation:

Anything raised to the #1/2# is equivalent to the square root of that value.

#-9^(1/2)#

#sqrt(-9)#

Now we have the square root of a negative number. We can change this into an imaginary number. The square root of a negative number is equal to that number #i#. For example:

#sqrt(- x) = x i#

So in this case:

#sqrt(-9) = 3i#

A08
Jun 30, 2016

#+-3i#

Explanation:

There is ambiguity in the question. To remove it let

  1. #-9^(1/2)# can be written as
    #-1xx9^(1/2)#
    #=>(-1)xx(+-3)#
    #=>+-3#
    As reverse is not true, hence supposition is not correct.
  2. #-9^(1/2)# can also be written as
    #(-1)^(1/2)xx9^(1/2)#
    #=>ixx+-3#
    #=+-3i#
    As reverse is always true

Hence #+-3i# is the correct answer.

Related questions
See all questions in Simplification of Radical Expressions
Impact of this question
5504 views around the world
You can reuse this answer
Creative Commons License