1Cademy - Perfect Square Numbers

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Square of a Number

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Perfect Square Numbers

A perfect square (also called a perfect square number) is the result of squaring a counting number. The perfect squares of the counting numbers $1$ through $15$ are:

$n$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$
$n^2$	$1$	$4$	$9$	$16$	$25$	$36$	$49$	$64$	$81$	$100$	$121$	$144$	$169$	$196$	$225$

Because multiplying two numbers with the same sign always yields a positive product, the square of any negative number equals the square of its positive counterpart. For instance, $(-8)^2 = 64$ and $8^2 = 64$ , so both produce the same perfect square. As a result, every perfect square is a positive number. Memorizing at least the first fifteen perfect squares makes it much easier to recognize square roots and to work with factoring in later algebra topics.

Updated 2026-04-21

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