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Properties of Perfect Squares

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Questions and Answers

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?

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.

zeros Signup and view all the answers

What is the result of squaring a proper fraction?

Smaller than the fraction Signup and view all the answers

Match the properties with their descriptions:

Property 1 = Number ending in 2, 3, 7, or 8 is never a perfect square Property 2 = Number ending in an odd number of zeros is never a perfect square Property 5 = The square of an even number is always even Property 6 = The square of an odd number is always odd Signup and view all the answers

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.