Difference between revisions of "2021 AMC 10B Problems/Problem 2"
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==Solution== | ==Solution== | ||
| − | Note that the square root of a squared number is the absolute value of the number. We know that <math>3-2\sqrt{3}</math> is actually negative, thus the absolute value is not <math>3-2\sqrt{3}</math> but <math>2\sqrt{3} - 3</math>. | + | Note that the square root of a squared number is the absolute value of the number because the square root function always gives a positive number. We know that <math>3-2\sqrt{3}</math> is actually negative, thus the absolute value is not <math>3-2\sqrt{3}</math> but <math>2\sqrt{3} - 3</math>. |
So the first term equals <math>2\sqrt{3}-3</math> and the second term is <math>3+2\sqrt3</math> | 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 and abhinavg0627 | Summed up you get <math>\boxed{\textbf{(D)} ~4\sqrt{3}}</math> ~bjc and abhinavg0627 | ||
Revision as of 19:36, 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 because the square root function always gives a positive number. We know that 
is actually negative, thus the absolute value is not but 
.
So the first term equals 
and the second term is 
Summed up you get 
~bjc and abhinavg0627
\phantom{no problem bjc}
Video Solution
https://youtu.be/HHVdPTLQsLc ~Math Python
