Difference between revisions of "1970 AHSME Problems/Problem 18"
(Created page with "== Problem == <math>\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}</math> is equal to <math>\text{(A) } 2\quad \text{(B) } 2\sqrt{3}\quad \text{(C) } 4\sqrt{2}\quad \text{(D) } \sqrt{6}...") |
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\text{(E) } 2\sqrt{2}</math> | \text{(E) } 2\sqrt{2}</math> | ||
| − | == Solution == | + | == Solution== |
| − | <math>\ | + | Square the expression: |
| + | |||
| + | <math>(\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}})^2=3+\sqrt{2}-2\sqrt{(3+\sqrt{2})(3-\sqrt{2})}+3-2\sqrt{2}=6-2\sqrt{9-8}=6-2\sqrt{1}=4</math> | ||
| + | |||
| + | <math>\Rightarrow\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}=\sqrt{4}=2\Rightarrow\boxed{A}</math> | ||
== See also == | == See also == | ||
| − | {{AHSME box|year=1970|num-b=17|num-a=19}} | + | {{AHSME 35p box|year=1970|num-b=17|num-a=19}} |
[[Category: Introductory Algebra Problems]] | [[Category: Introductory Algebra Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 15:23, 2 July 2016
Problem
is equal to
Solution
Square the expression:
See also
| 1970 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 17 |
Followed by Problem 19 | |
| 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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
