Practice free →
HomeGRE › Quantitative Reasoning › Which of the following correctly evaluates $\sqr…

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 $10$).
Solve this in the app — GRE practice & 24k+ MCQs →
Related questions