Difference between revisions of "2021 AMC 10B Problems/Problem 2"
| Line 1: | Line 1: | ||
| − | + | ==Problem== | |
| − | What is the value of <cmath>\sqrt{(3-2\sqrt{ | + | What is the value of <cmath>\sqrt{(3-2\sqrt{3})^2}+\sqrt{(3+2\sqrt{3})^2}?</cmath> |
<math>\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</math> | <math>\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</math> | ||
| − | + | ==Solution== | |
| − | + | Note that the square root of a squared number is the absolute value of the number. | |
| − | + | So the first term equals <math>2\sqrt{3}-3</math> and the second term is <math>3+2\sqrt3</math> | |
| + | Summed up you get <math>\boxed{\textbf{(D)} ~4\sqrt{3}}</math>~bjc | ||
Revision as of 17:29, 11 February 2021
Problem
What is the value of ![\[\sqrt{(3-2\sqrt{3})^2}+\sqrt{(3+2\sqrt{3})^2}?\]](http://latex.artofproblemsolving.com/6/c/1/6c10ec9f88ac0dc6c038e3f5b7062a60ea2444f0.png)
Solution
Note that the square root of a squared number is the absolute value of the number.
So the first term equals 
and the second term is 
Summed up you get 
~bjc
