Difference between revisions of "1986 AHSME Problems/Problem 5"
(Created page with "==Problem== Simplify <math>\left(\sqrt[6]{27} - \sqrt{6 \frac{3}{4} }\right)^2</math> <math>\textbf{(A)}\ \frac{3}{4} \qquad \textbf{(B)}\ \frac{\sqrt 3}{2} \qquad \textbf{(C)}...") |
(Added a solution with explanation) |
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==Solution== | ==Solution== | ||
− | + | We have <math>\sqrt[6]{27} = (3^{3})^(\frac{1}{6}) = 3^{\frac{1}{2}} = \sqrt{3}</math> and <math>\sqrt{6 \frac{3}{4}} = \sqrt{\frac{27}{4}} = \frac{3 \sqrt{3}}{2}</math>, so the answer is <math>(\sqrt{3} - \frac{3 \sqrt{3}}{2})^{2} = (-\frac{\sqrt{3}}{2})^{2} = \frac{3}{4}</math>, which is <math>\boxed{A}</math>. | |
== See also == | == See also == |
Revision as of 18:09, 1 April 2018
Problem
Simplify
Solution
We have and
, so the answer is
, which is
.
See also
1986 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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 | ||
All AHSME Problems and Solutions |
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