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Simplifying and
To simplify an expression of the form where is a perfect square, first evaluate the principal (positive) square root, then apply the negative sign in front:
: The negative sign sits in front of the radical, not underneath it. Evaluate the square root first: because . Then apply the negation: .
: Again, the negative sign is in front of the radical. Evaluate the square root first: because . Then apply the negation: .
In both cases the procedure is the same: recognize the radicand as a perfect square, find its principal square root, and then take the opposite of that result. The key observation is that the negative sign is not part of the radicand — it is applied after the square root has been computed.
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