Consider a two digit number AB
Where:
A+B = C
C x C = A B
What is A B ?
Details and assumptions:
Each letter represents one numerical digit. AB does not indicate multiplication. AB is positive.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
It is given that the number A B is two digits and a perfect square.
There are only six numbers that are two-digit perfect squares: 1 6 , 2 5 , 3 6 , 4 9 , 6 4 , 8 1 .
From the problem statement, A B must also satisfy the condition: ( A + B ) 2 = A B .
Testing each of the six perfect squares, only 8 1 satisfies this condition: ( 8 + 1 ) 2 = 8 1 .
Hence, A B = 8 1 .
Because AB is a 2-digit number:
9
<
A
B
=
C
2
=
(
A
+
B
)
2
<
1
0
0
So AB must be 16, 25, 36, 49, 64 or 81 (squares of 4,5,6,7,8,9).
And we have
3
<
A
+
B
<
1
0
So we get rid of 49 and 64, as their A+B > 10.
(
A
+
B
)
2
=
(
8
+
1
)
2
=
9
2
=
8
1
So it's 81.
(I know it looks like Alvi Newaz's solution, I just want to make it clearer and somehow easier)
Problem Loading...
Note Loading...
Set Loading...
C*C=AB so 9<C^2<100. So just find the squares of 4,5,6,7,8,9 and one of these is the solution.