Which statement describes a perfect square?

Which statement describes a perfect square?

• A. Multiplying two consecutive primes
• B. Taking a positive integer and multiplying it by itself
• C. The sum of two squares
• D. The product of a number and its reciprocal

Answer: (B)

A perfect square is a number that can be written as n^2 for some integer n. If you take a positive integer and multiply it by itself, you’re directly forming n^2, which is exactly what a perfect square is. For example, 3×3 is 9, and 7×7 is 49, both perfect squares. The other descriptions don’t define squares in general. Multiplying two consecutive primes usually gives a number whose prime factors occur to the first power, not squared, so it’s not guaranteed to be a square. The sum of two squares isn’t always a square either, so that description doesn’t consistently produce perfect squares. The product of a number and its reciprocal equals 1 for any nonzero number, which is a single value and does not characterize all perfect squares.

A perfect square is a number that can be written as n^2 for some integer n. If you take a positive integer and multiply it by itself, you’re directly forming n^2, which is exactly what a perfect square is. For example, 3×3 is 9, and 7×7 is 49, both perfect squares.

The other descriptions don’t define squares in general. Multiplying two consecutive primes usually gives a number whose prime factors occur to the first power, not squared, so it’s not guaranteed to be a square. The sum of two squares isn’t always a square either, so that description doesn’t consistently produce perfect squares. The product of a number and its reciprocal equals 1 for any nonzero number, which is a single value and does not characterize all perfect squares.