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Questions and Answers
What is the result of dividing a number by 3 if it is not a perfect square?
What happens when a number is divided by 4 if it is not a perfect square?
Leaves a remainder 2 or 3
The square of an even number is always odd.
False
A number ending in an odd number of _______________ is never a perfect square.
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What is the result of squaring a proper fraction?
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Match the properties with their descriptions:
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Study Notes
Properties of Perfect Squares
- A number ending in 2, 3, 7, or 8 is never a perfect square.
- A number ending in an odd number of zeros is never a perfect square.
- If a number when divided by 3 leaves a remainder of 2, then it is not a perfect square.
- If a number when divided by 4 leaves a remainder of 2 or 3, then it is not a perfect square.
Properties of Squares of Even and Odd Numbers
- The square of an even number is always even.
- Examples: 2^2 = 4, 4^2 = 16, 6^2 = 36, 8^2 = 64, etc.
- The square of an odd number is always odd.
- Examples: 1^2 = 1, 3^2 = 9, 5^2 = 25, 7^2 = 49, 9^2 = 81, etc.
Properties of Squares of Fractions
- The square of a proper fraction is smaller than the fraction.
- Example: (2/3)^2 = (2/3 * 2/3) = 4/9 and 4/9 < 2/3 since (4 * 3) < (9 * 2)
Property of Natural Numbers
- For every natural number n, we have (n + 1)^2 - n^2 = (2n + 1)
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Description
Learn about the properties of perfect squares, including rules about numbers ending in 2, 3, 7, or 8, and those with an odd number of zeros, as well as divisibility by 3.
