Difference between revisions of "2021 AMC 10B Problems/Problem 2"

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We have that <math>\sqrt{(3-2\sqrt{2})^2} = 3-2\sqrt{2}</math> and <math>\sqrt{(3+2\sqrt{2})^2} = 3+2\sqrt{2}</math>. Adding them together, we get that it is equal to <math>6</math>.

Revision as of 18:28, 11 February 2021

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

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

~~Solution~~

We have that $\sqrt{(3-2\sqrt{2})^2} = 3-2\sqrt{2}$ and $\sqrt{(3+2\sqrt{2})^2} = 3+2\sqrt{2}$. Adding them together, we get that it is equal to $6$.

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