2019 Mock AMC 10B Problems/Problem 3: Difference between revisions
Created page with "After trying each option we have <cmath></cmath>A) <math>3^(2018/3)</math> which isn't rational as 2018 is not divisible by 3 <cmath></cmath>B) <math>3^(2019/2)</math> which..." |
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After trying each option we have | After trying each option we have | ||
<cmath></cmath>A) <math>3^(2018/3)</math> which isn't rational as 2018 is not divisible by 3 | <cmath></cmath>A) <math>3^(2018/3)</math> which isn't rational as 2018 is not divisible by 3<math> | ||
<cmath></cmath>B) <math>3^(2019/2)< | <cmath></cmath>B) </math>3^(2019/2)<math> which isn't rational as 2019 isn't divisible by 2</math> | ||
<cmath></cmath>C) <math>3^2+\sqrt{2}^2+6\sqrt{2}</math> which equals <math>11+6\sqrt{2}</math> which is irrational | <cmath></cmath>C) <math>3^2+\sqrt{2}^2+6\sqrt{2}</math> which equals <math>11+6\sqrt{2}</math> which is irrational<math> | ||
<cmath></cmath>D) <math>(2pi)^2< | <cmath></cmath>D) </math>(2pi)^2<math> equals </math>4pi^2<math> which is irrational</math> | ||
<cmath></cmath>E) <math>(3-\sqrt{2})(3+\sqrt{2})=9-2=7</math> which is rational | <cmath></cmath>E) <math>(3-\sqrt{2})(3+\sqrt{2})=9-2=7</math> which is rational<math> | ||
We have <math>\boxed{\bold{E}}< | We have </math>\boxed{\bold{E}}<math> </math>(3-\sqrt{2})(3+\sqrt{2})$ | ||
Revision as of 23:36, 22 September 2019
After trying each option we have
![\[\]](http://latex-new.aopstest.com/5/7/f/57f1406b65f9f2e6a365b7356da731780b42cceb.png)
A) 
which isn't rational as 2018 is not divisible by 3
3^(2019/2)
C) 
which equals 
which is irrational
(2pi)^2
4pi^2
E) 
which is rational
\boxed{\bold{E}}$$ (Error compiling LaTeX. Unknown error_msg)(3-\sqrt{2})(3+\sqrt{2})$
