SOLUTION: What is the smallest positive integer which multiplied by 40 gives a perfect square? (A) 2 (B) 5 (C) 20 (D) 40 (E) None of these

Question 297621: What is the smallest positive integer which multiplied by 40 gives a perfect square?
(A) 2 (B) 5 (C) 20 (D) 40 (E) None of these
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
A perfect square is an integer that is the result of the squaring of another integer.

25 would be a perfect square because it is the result of 5*5

169 would be a perfect square because it is the result of 13*13

the factors of the perfect square can be positive or negative.

Example

5*5 = 25

(-5)*(-5) = 25

Both 5 and -5 are square roots of the perfect square of 25.

In your problem:

square root of (2*40) = square root of 80 = 8.94427191 (not an integer)

square root of (5*40) = square root of 200 = 14.14213562 (not an integer)

square root of (20*40) = square root of 800 = 28.28427125 (not an integer)

square root of (40*40) = square root of 1600 = 40 (this is the perfect square)

Answer is selection D.

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