How do you simplify the square root #-sqrt25#?

Answer 1

Strictly speaking, #-sqrt25=pm5#. However, if the notation is to let us know the desired sign of the result, it's simply #-5#

#-sqrt25=(-1)sqrt25#

Remember that the square root operation is the opposite of the square operation, and so when they both occur, they cancel.

We can get a product of 25 when we square #5 ->(5^2=25)# and when we square #-5->((-5)^2=25)#. And so the square root of 25 can be 5 and it can be #-5#. We write down both results:

#-sqrt25=(-1)sqrt25=(-1)(pm5)=pm5#

Sometimes it's understood that the sign in front of the square root indicates the sign desired. And so the answer in this case could also be simply #-5#

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Answer 2

Julian Avila

The square root of -25 is a complex number and cannot be simplified within the realm of real numbers. However, in the context of complex numbers, it can be simplified as ( 5i ), where ( i ) represents the imaginary unit.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.