Perfect Square Calculator

Enter any whole number into the Perfect Square Calculator and find out whether it's a perfect square. You'll see the square root, the nearest perfect squares below and above your number, and a clear verdict — all calculated from a single number input. Also try the GCF Calculator (Greatest Common Factor).

Enter any non-negative whole number to check if it is a perfect square.

Results

Is It a Perfect Square?

--

Square Root

--

Integer Square Root (Floor)

--

Nearest Perfect Square Below

--

Nearest Perfect Square Above

--

Perfect Square (n × n)

--

Results Table

Frequently Asked Questions

What is a perfect square number?

A perfect square is a number that can be expressed as the product of two identical integers. For example, 49 is a perfect square because 7 × 7 = 49. The square root of a perfect square is always a whole number (integer). See also our calculate Prime Factorization (Exponential Form), Prime Factors (comma separated) & Number of Distinct Prime Factors — Prime Factorization.

How do I check if a number is a perfect square?

Take the square root of the number and check whether the result is a whole number. If √n is an integer, then n is a perfect square. For example, √36 = 6 (integer), so 36 is a perfect square. √50 ≈ 7.071 (not an integer), so 50 is not a perfect square.

What is the square if the root is 6?

If the square root is 6, then the perfect square is 6 × 6 = 36. Any integer n multiplied by itself gives the perfect square n².

Is 0 a perfect square?

Yes, 0 is considered a perfect square because 0 × 0 = 0. Its square root is 0, which is a whole number (integer), satisfying the definition of a perfect square. You might also find our find Modular Multiplicative Inverse (a⁻¹ mod m) with Multiplicative Inverse Modulo Calculator useful.

Are perfect squares rational or irrational numbers?

Perfect squares are always rational numbers. Since their square roots are integers, they can be expressed as a ratio of two integers, making them rational. Non-perfect squares like 2 or 3 have irrational square roots (like √2 ≈ 1.4142...).

How many perfect squares are there between 1 and 100?

There are 10 perfect squares between 1 and 100: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. In general, there are exactly n perfect squares from 1 to n².

Can a negative number be a perfect square?

No, negative numbers cannot be perfect squares in the realm of real numbers. Since any real number multiplied by itself yields a non-negative result, perfect squares are always zero or positive. In complex numbers, the concept extends differently, but conventionally perfect squares are non-negative.

What is the difference between a perfect square and a perfect square trinomial?

A perfect square number is an integer that is the square of another integer (e.g., 25 = 5²). A perfect square trinomial is a polynomial expression in the form ax² + bx + c that can be factored into the square of a binomial, such as (x + 3)² = x² + 6x + 9. They are related concepts but apply to numbers and polynomials respectively.