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Simplifying , , , and
Simplify each expression by recognizing the radicand as a perfect square and, when a negative sign appears in front of the radical, applying it after evaluating the principal square root.
ⓐ : Since , the principal square root of is .
ⓑ : Since , the principal square root of is .
ⓒ : The negative sign sits in front of the radical, not under it. Evaluate the principal square root first: because . Then apply the negation to obtain .
ⓓ : Again, the negative sign is placed before the radical. Evaluate the square root first: because . Then apply the negation to obtain .
Parts ⓐ and ⓑ are straightforward evaluations of the principal square root. Parts ⓒ and ⓓ reinforce that a negative sign in front of the radical means "take the opposite of the principal square root" — the negation is applied only after the square root has been computed.
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Simplifying , , , and
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Example of Simplifying
Example of Simplifying , , and
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