2021 AMC 10B Problems/Problem 2: Difference between revisions

Revision as of 17:28, 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 $6$ .

Revision as of 17:26, 11 February 2021 view source Bjc (talk \| contribs) editor 110 edits mNo edit summary ← Older edit		Revision as of 17:28, 11 February 2021 view source Arduinorasp34567 (talk \| contribs) 2 edits No edit summary Newer edit →
Line 5:		Line 5:

	~~Solution~~		~~Solution~~

			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>.

Page

Toolbox

Search

2021 AMC 10B Problems/Problem 2: Difference between revisions

Revision as of 17:28, 11 February 2021