Difference between revisions of "2021 AMC 10A Problems/Problem 1"
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\end{align*}</cmath> | \end{align*}</cmath> | ||
-[[User:PureSwag|PureSwag]] | -[[User:PureSwag|PureSwag]] | ||
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+ | ==Solution 4 (When you have too much time) == | ||
+ | |||
+ | Using the difference of squares, we have <cmath>(2-\sqrt{2})(2+\sqrt{2}) - (3-\sqrt{3})(3+\sqrt{3}) + (4-2)(4+2).</cmath> | ||
+ | Knowing that <math>\sqrt{2} \approx 1.41</math> and <math>\sqrt{3} \approx 1.73,</math> we get <cmath>(2-\sqrt{2})(2+\sqrt{2}) - (3-\sqrt{3})(3+\sqrt{3}) + (4-2)(4+2) \approx 0.59\cdot 3.41 -1.26\cdot 4.73 + 2 \cdot 6 | ||
+ | =8.0521,</cmath> which is closest to <math>\boxed{\textbf{(D) } 8}.</math> | ||
==Video Solution 1 (Lightning Fast)== | ==Video Solution 1 (Lightning Fast)== | ||
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~ThePuzzlr | ~ThePuzzlr | ||
− | == Video Solution 5 (Arithmetic Computation) == | + | == Video Solution 5 by OmegaLearn (Arithmetic Computation) == |
https://youtu.be/0VvM_f-IDvE | https://youtu.be/0VvM_f-IDvE | ||
Latest revision as of 19:22, 14 October 2024
Contents
- 1 Problem
- 2 Solution 1
- 3 Solution 2
- 4 Solution 3 (Overkill: Just for Fun)
- 5 Solution 4 (When you have too much time)
- 6 Video Solution 1 (Lightning Fast)
- 7 Video Solution 2
- 8 Video Solution 3 (Very Very Quick Computation)
- 9 Video Solution 4 (Quick Computation)
- 10 Video Solution 5 by OmegaLearn (Arithmetic Computation)
- 11 Video Solution 6
- 12 Video Solution 7
- 13 Video Solution 8 (Problems 1-3)
- 14 Video Solution 9
- 15 See Also
Problem
What is the value of
Solution 1
This corresponds to
-happykeeper
Solution 2
We have ~MRENTHUSIASM
Solution 3 (Overkill: Just for Fun)
We have -PureSwag
Solution 4 (When you have too much time)
Using the difference of squares, we have Knowing that and we get which is closest to
Video Solution 1 (Lightning Fast)
~ Education, the Study of everything
Video Solution 2
Video Solution 3 (Very Very Quick Computation)
https://www.youtube.com/watch?v=m0_UMI2mnZs&list=PLexHyfQ8DMuKqltG3cHT7Di4jhVl6L4YJ&index=2 ~North America Mathematic Contest Go Go Go
Video Solution 4 (Quick Computation)
https://youtu.be/C3n2hgBhyXc?t=37 ~ThePuzzlr
Video Solution 5 by OmegaLearn (Arithmetic Computation)
~ pi_is_3.14
Video Solution 6
~savannahsolver
Video Solution 7
~IceMatrix
Video Solution 8 (Problems 1-3)
~MathWithPi
Video Solution 9
~TheLearningRoyal
See Also
2021 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.