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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 is the result of dividing a number by 3 if it is not a perfect square?
- No remainder
- Remainder 2 (correct)
- Remainder 1
- Remainder 3
What happens when a number is divided by 4 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.
The square of an even number is always odd.
False (B)
A number ending in an odd number of _______________ is never a perfect square.
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?
What is the result of squaring a proper fraction?
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Match the properties with their descriptions:
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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