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Questions and Answers
A ______ is a number that can be expressed as the square of an integer.
perfect square
The ______ of an integer is always a perfect square.
square
Perfect squares always end in 0, 1, 4, 5, 6, or ______.
9
If a number ends in 1, it is a perfect square if and only if the number formed by its last two digits minus ______ is divisible by 4.
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If a number ends in 4, it is a perfect square if and only if the number formed by its last two digits minus ______ is divisible by 4.
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The ______ root of a perfect square is always an integer.
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Study Notes
Perfect Squares
Definition
- A perfect square is a number that can be expressed as the square of an integer
- Example: 16 is a perfect square because it can be expressed as 4²
Properties
- The square of an integer is always a perfect square
- The square root of a perfect square is always an integer
- Perfect squares always end in 0, 1, 4, 5, 6, or 9
Examples
- 1, 4, 9, 16, 25, 36, 49, 64, ...
- These numbers can be expressed as 1², 2², 3², 4², 5², 6², 7², 8², ...
Identifying Perfect Squares
- If a number ends in 0, it is a perfect square if and only if the number formed by its last two digits is a perfect square
- If a number ends in 1, it is a perfect square if and only if the number formed by its last two digits minus 1 is divisible by 4
- If a number ends in 4, it is a perfect square if and only if the number formed by its last two digits minus 4 is divisible by 4
- If a number ends in 5, it is a perfect square if and only if the number formed by its last two digits minus 5 is divisible by 4
- If a number ends in 6, it is a perfect square if and only if the number formed by its last two digits minus 6 is divisible by 4
- If a number ends in 9, it is a perfect square if and only if the number formed by its last two digits minus 9 is divisible by 4
Perfect Squares
Definition
- A perfect square is a number that can be expressed as the square of an integer.
- Example: 16 is a perfect square because it can be expressed as 4².
Properties
- The square of an integer is always a perfect square.
- The square root of a perfect square is always an integer.
- Perfect squares always end in 0, 1, 4, 5, 6, or 9.
Examples
- 1, 4, 9, 16, 25, 36, 49, 64,... are perfect squares.
- These numbers can be expressed as 1², 2², 3², 4², 5², 6², 7², 8²,...
Identifying Perfect Squares
- If a number ends in 0, it is a perfect square if and only if the number formed by its last two digits is a perfect square.
- If a number ends in 1, it is a perfect square if and only if the number formed by its last two digits minus 1 is divisible by 4.
- If a number ends in 4, it is a perfect square if and only if the number formed by its last two digits minus 4 is divisible by 4.
- If a number ends in 5, it is a perfect square if and only if the number formed by its last two digits minus 5 is divisible by 4.
- If a number ends in 6, it is a perfect square if and only if the number formed by its last two digits minus 6 is divisible by 4.
- If a number ends in 9, it is a perfect square if and only if the number formed by its last two digits minus 9 is divisible by 4.
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Description
Learn about perfect squares, their definition, properties, and examples in this quiz. Test your knowledge of math concepts!
