Is N a Perfect Square? Calculator
Perfect Square Checker
Use the checker above to determine whether any non-negative integer is a perfect square. A perfect square is a non-negative integer that can be written as the product of an integer with itself: n = k² for some integer k. The first perfect squares are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, ...
What Is a Perfect Square?
A perfect square is a non-negative integer that is the square of an integer:
n is a perfect square ⇔ n = k2, k ∈ ℤ≥0
Equivalently, n is a perfect square if and only if √n is an integer. Geometrically, you can arrange n identical unit squares into a square grid only if n is a perfect square.
Prime-factorization rule: n is a perfect square iff every prime in the prime factorization of n appears with an even exponent. For example, 144 = 24 × 32 (both even) is a perfect square; 72 = 23 × 32 has an odd exponent on 2, so it is not.
Common Examples
Perfect Squares from 1 to 100
The numbers 1, 4, 9, 16, ..., 100 are the perfect squares from 1² to 10². Click any number below to see its check page.
Popular Perfect-Square Checks
Common ‘Is N a perfect square?’ queries — click any to see the step-by-step verdict:
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