Which of the following correctly evaluates $\sqrt{100}$ in the real number system?
A$\pm 10$
B$10$ only (the **nonnegative** square root)
C$-10$ only
DUndefined for $100$
Answer & Solution
Correct answer: B. $10$ only (the **nonnegative** square root)
By convention, the **radical symbol** $\sqrt{}$ denotes the **nonnegative** square root of a nonnegative number. So $\sqrt{100} = 10$, not $\pm 10$.
The number $100$ does have two square roots — $10$ and $-10$ — but the **expression** $\sqrt{100}$ refers only to the positive one. To get the negative root we write $-\sqrt{100} = -10$.
- Trap A confuses *the square roots of 100* with *the value of the expression $\sqrt{100}$*.
- Trap C reverses the convention.
- Trap D is wrong — $100$ is a perfect square; only square roots of *negative* numbers are undefined in the reals.
This distinction matters when solving equations like $x^{2} = 100$ (gives both $\pm 10$) vs. evaluating an expression like $\sqrt{100}$ (gives just $10$).
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