Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.6 AIME Find the answer

1. If the cube root of $\sqrt{125}$ is $A$ , and the square root of $\sqrt{25}$ is $B$ . Then $A+B=(\quad)$ .

Pick one

Solution

-1. A.
Since the cube root of $\sqrt{125}$ is $\sqrt{5}$ , and the square root of $\sqrt{25}$ is $\pm \sqrt{5}$ , therefore, $A+B=2 \sqrt{5}$ or 0.

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