Perfect Squares

[baily106]

Hello,

This problem is from NOVA's Math Book.
It states: "A perfect square is a number that becomes an integer when square rooting it. A,B,C are three positive integers. The ratio of the three numbers is 1:2:3, respectively. Which one of the following expressions must be a perfect square?

A) A+B+C
B) A^2+B^2+C^2
C) A^3+B^3+C^3
D)3A^2+B^2+C^2
E)3A^2+4B^2+4C^2

Thanks.

[tommywallach]

Hey Baily,

Try numbers:

1, 2, 3

a) 1 + 2 + 3 = 6 (not perfect square)
b) 1 + 4 + 9 = 14 (not perfect square)
c) 1 + 8 + 27 = 36 (perfect square!)
d) 3 + 4 + 9 = 16 (perfect square!)
e) 3 + 16 + 36 = 55 (not perfect square)

Now we just need to check c and d. Let's use 2, 4, and 6:

c) 8 + 64 + 216 = 288 (not a perfect square)
d) 12 + 16 + 36 = 64 (perfect square!)

the answer is (d).

-t

[baily106]

Thanks.

[tommywallach]

NP.