Difference between revisions of "2019 Mock AMC 10B Problems/Problem 3"
(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^ | + | <cmath></cmath>A) <math>3^\frac{2018}{3}</math> which is irrational as 2018 is not divisible by 3 |
− | <cmath></cmath>B) <math>3^ | + | <cmath></cmath>B) <math>3^\frac{2019}{2}</math> which is irrational as 2019 isn't divisible by 2 |
<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 | ||
− | <cmath></cmath>D) <math>(2pi)^2</math> equals <math>4pi^2</math> which is irrational | + | <cmath></cmath>D) <math>(2pi)^2</math> equals <math>4pi^2</math>, which is irrational |
<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 | ||
We have <math>\boxed{\bold{E}}</math> <math>(3-\sqrt{2})(3+\sqrt{2})</math> | We have <math>\boxed{\bold{E}}</math> <math>(3-\sqrt{2})(3+\sqrt{2})</math> |
Latest revision as of 11:47, 5 November 2019
After trying each option we have
A)
which is irrational as 2018 is not divisible by 3
B)
which is irrational as 2019 isn't divisible by 2
C)
which equals
which is irrational
D)
equals
, which is irrational
E)
which is rational
We have