2021 AMC 10B Spring Problem 2 — Solution | LIVE by Po-Shen Loh

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2021 AMC 10B Spring Problem 2

Attempt Problem 2 of the 2021 AMC 10B Spring below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 10B Spring solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

2.

What is the value of $\begin{aligned} &\sqrt{\left(3-2\sqrt{3}\right)^2} \\ &{}+\sqrt{\left(3+2\sqrt{3}\right)^2}? \end{aligned}$

$0$

$4\sqrt{3}-6$

$6$

$4\sqrt{3}$

$4\sqrt{3}+6$

Answer: D

Concepts:radical absolute value

Difficulty rating: 770

Solution:

Because $\sqrt{u^2}=|u|,$ the expression equals $|3-2\sqrt3|+|3+2\sqrt3|.$ Since $2\sqrt3>3,$ this becomes $(2\sqrt3-3)+(3+2\sqrt3)=4\sqrt3.$

Thus, the correct answer is D .

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