Question

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`

Explanation:

`-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`