Perfect Square Calculator
Use our perfect square calculator to calculate perfect square values and check if a number is a perfect square. Learn what a perfect square is in math, how to find perfect square numbers, perfect square formula and perfect square method ideas (including completing the square), plus perfect square equation examples like is 1 perfect square.
What is a Perfect Square?
A perfect square is a number that can be written as an integer multiplied by itself. For example, 25 is a perfect square because 25 = 5 × 5.
In math, perfect square values come from n² where n is an integer: 1, 4, 9, 16, 25, 36, and so on.
This perfect square calculator can help you calculate perfect square values (n²) and determine whether a given number is a perfect square.
Perfect Square Formula and Method
Perfect squares are generated by squaring integers. Another common “perfect square method” topic is completing the square, which rewrites a quadratic as a perfect square expression.
If a number equals n^2 for some integer n, it is a perfect square.
Examples: √36 = 6 (integer) so 36 is a perfect square.
This is the key identity used in the perfect square method for quadratics.
Squaring an integer produces a perfect square.
A trinomial that factors to a binomial squared is a perfect square expression.
How to Use the Perfect Square Calculator
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Enter a number to check, or enter an integer n to calculate n² (a perfect square value).
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The calculator determines whether the input is a perfect square by checking if the square root is an integer.
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If it is a perfect square, you’ll see the square root (the integer that squares to it).
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If it is not, you’ll see that it’s not a perfect square (and an approximate square root, if applicable).
Frequently Asked Questions
A number is a perfect square if it can be written as n² for an integer n. A quick test is whether √x is an integer.
Yes. 1 = 1², so it is a perfect square.
Pick an integer n and square it: n² = n·n. The result is a perfect square value.
Use the square root function: if √x is a whole number, then x is a perfect square. Or use an x² key to compute n².
They are numbers like 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, and so on (n² for integers n).
Perfect squares come from n². In algebra, perfect square trinomials match a² ± 2ab + b² = (a ± b)².
Rewrite x² + bx by adding (b/2)²: x² + bx + (b/2)² = (x + b/2)². For ax² + bx + c, factor out a first.
Perfect squares are integers, which are rational numbers. Also, the square root of a perfect square is an integer (therefore rational).