Which of the following is a perfect square?

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Prepare for the CSET Multiple Subjects Subtest 2. Dive into math and science with flashcards and multiple choice questions, each question offering hints and explanations. Gear up for your success!

Multiple Choice

Which of the following is a perfect square?

Explanation:
A perfect square is a number that can be written as an integer squared, so its square root is an integer. For 9, the square root is 3, which is an integer, so 9 is a perfect square. The other numbers don’t have integer square roots: sqrt(12) ≈ 3.464, sqrt(18) ≈ 4.243, and sqrt(27) ≈ 5.196. From prime factorization, 9 = 3^2 has all exponents even, while 12 = 2^2·3, 18 = 2·3^2, and 27 = 3^3 have an odd exponent, so they’re not perfect squares. Therefore, the only perfect square here is 9.

A perfect square is a number that can be written as an integer squared, so its square root is an integer. For 9, the square root is 3, which is an integer, so 9 is a perfect square. The other numbers don’t have integer square roots: sqrt(12) ≈ 3.464, sqrt(18) ≈ 4.243, and sqrt(27) ≈ 5.196. From prime factorization, 9 = 3^2 has all exponents even, while 12 = 2^2·3, 18 = 2·3^2, and 27 = 3^3 have an odd exponent, so they’re not perfect squares. Therefore, the only perfect square here is 9.

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