Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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

m
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>.

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 $6$.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2021_AMC_10B_Problems/Problem_2&oldid=145302"