MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AIME Problems
2006 AIME Problems
5
Square Roots
Square Roots
Source: 2006 AIME A Problem 5
March 9, 2006
USAMTS
AMC
Radicals
Problem Statement
The number
104
6
+
468
10
+
144
15
+
2006
\sqrt{104\sqrt{6}+468\sqrt{10}+144\sqrt{15}+2006}
104
6
+
468
10
+
144
15
+
2006
can be written as
a
2
+
b
3
+
c
5
,
a\sqrt{2}+b\sqrt{3}+c\sqrt{5},
a
2
+
b
3
+
c
5
,
where
a
,
b
,
a, b,
a
,
b
,
and
c
c
c
are positive integers. Find
a
⋅
b
⋅
c
a\cdot b\cdot c
a
⋅
b
⋅
c
.
Back to Problems
View on AoPS