2021 AMC 10B Problems/Problem 2

Revision as of 18:54, 11 February 2021 by Pc05 (talk | contribs) (Solution)

Problem

What is the value of \[\sqrt{(3-2\sqrt{3})^2}+\sqrt{(3+2\sqrt{3})^2}?\]

$\textbf{(A)} ~0 \qquad\textbf{(B)} ~4\sqrt{3}-6 \qquad\textbf{(C)} ~6 \qquad\textbf{(D)} ~4\sqrt{3} \qquad\textbf{(E)} ~4\sqrt{3}+6$

Solution

Note that the square root of a squared number is the absolute value of the number. So the first term equals $2\sqrt{3}-3$ and the second term is $3+2\sqrt3$ Summed up you get $\boxed{\textbf{(D)} ~4\sqrt{3}}$ ~bjc

$\phantom{Sorry whoever's solution I overrided, the problem should have \sqrt{3} not \sqrt{2}}$

Video Solution

https://youtu.be/HHVdPTLQsLc ~Math Python

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