Perfect Square Calculator

Enter any whole number to check if it is a perfect square, with its square root and prime factorization.

Examples:144501,2251,000

Yes, 144 is a perfect square. Its square root is the whole number 12.

Square root

√144 = 12, because 12 × 12 = 144

Next perfect square

13² = 169

Prime factorization

144 = 2432

Every exponent is even, so the number is a perfect square.

What Is a Perfect Square?

A perfect square is a whole number that equals another whole number multiplied by itself. 144 is a perfect square because 12 × 12 = 144. The numbers 1, 4, 9, 16, 25 and 36 are the first few.

How to Use This Perfect Square Calculator

  1. Type any whole number into the box.
  2. Press Calculate to see whether it is a perfect square, its square root, its prime factorization and its simplest radical form.

How to Check if a Number Is a Perfect Square

  1. Find the square root of the number.
  2. If the square root is a whole number, the number is a perfect square.
  3. Or write the number as a product of primes. If every exponent is even, it is a perfect square.
Handwritten notebook page showing 144 is a perfect square because 12 times 12 equals 144
144 = 2⁴ × 3². Both exponents are even, so 144 = 12 × 12 is a perfect square.

Simplest Radical Form

When a number is not a perfect square, you can still pull its square factors out of the root. 50 = 2 × 5², so √50 = 5√2.

Handwritten notebook page simplifying the square root of 50 to 5 times the square root of 2
50 = 2 × 5², so √50 = 5√2, which is about 7.0711.

Worked Examples

Common mistakes

Perfect Square Calculator FAQs

What is a perfect square?

A perfect square is a whole number that is the square of another whole number. For example, 144 is a perfect square because 12 × 12 = 144.

How do you know if a number is a perfect square?

Find its square root. If the square root is a whole number, the number is a perfect square. You can also write it as a product of primes: if every exponent is even, it is a perfect square.

Is 50 a perfect square?

No. The square root of 50 is about 7.0711, and 50 lies between 7² = 49 and 8² = 64. Its simplest radical form is 5√2.

Is 1 a perfect square?

Yes. 1 × 1 = 1, so 1 is the smallest positive perfect square.

Is 0 a perfect square?

Yes, 0 × 0 = 0. This calculator works with positive whole numbers, so it starts from 1.

What are the first perfect squares?

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144.

Why do perfect squares have an odd number of factors?

Factors come in pairs, but in a perfect square the middle factor pairs with itself. For 36, the factor 6 pairs with 6, so 36 has 9 factors.

What is the simplest radical form?

It pulls every square out of the root. For 50 = 2 × 5², the 5² comes out as 5, which leaves 5√2.

More Worked Examples

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