Looking for the ideal square calculator? Check out our simple tool to see if your number is among the illustrious list of perfect squares.

Check out our post below to learn the definition of the perfect square and calculate it in a few simple steps.

## What is a perfect square number?

A perfect square number can be made by **multiplying two identical integers**; in other words, the root of a perfect square is a whole number.

An integer is a whole number that can be negative, positive, or equal to zero. Fractions and decimals aren’t allowed in integers.

• Integer examples are -5, 0, 3, and 235.

• Examples of non-integer numbers: 1.2, 334, 0.25.

Are you looking for a different sort of perfect square calculator? A perfect square trinomial is defined as ax2 + bx + c. The b2 = 4ac criterion should also be satisfied by this formula.

## How to use the perfect square calculator?

This section will walk you through the processes of using the perfect square calculator.

**Your input**

You may input whatever number you like, of any length and value (well, up to a point). Don’t be afraid to input entire equations; try multiplication (5*67), division (3/675), addition (1+1), or subtraction (1.56-0.86).

**Your outcome**

Our complete square calculator will give a straightforward, step-by-step explanation in addition to a basic remark regarding whether your number is a perfect square or not.

## How to calculate a perfect square?

To validate the accuracy of your square, just compute the **square root** of a given value. Your number is the perfect square if the square root is an integer.

Let’s compute the squares of these numbers: The numbers 25 and 66.

√25 = 5 – 5 is an integer, and 25 is a perfect square.

√66 = 8.1240384 – 8.1240384 is not an integer – 53 is not a perfect square

What if you don’t have a calculator and your number is large?

Let’s try something a little more exciting:

It’s useful to know that all **perfect squares conclude** with the numbers 1, 4, 5, 6, 9, or 00. That’s how you may make a quick initial choice and determine which numbers can and cannot be perfect squares.

If your number finishes in 1, 4, or 9, the tenth digit should always be even (0, 2, 4, 6, 8) in order for it to be a perfect square.

When your number finishes in a 5, the tenth digit is always 2.

If your number finishes with a six, the tenth digit is always odd (1, 3, 5, 7, and 9)

We must also remember that the digital root of the integer must be 0, 1, 4, or 7. Your number cannot be a perfect square if the computed digital root is not one of the values above.

We may simply compute the digital root of a number by adding all of its digits and then summarizing them if the resultant total contains two digits. (For example, 1234567 1+2+3+4+5+6+7 = 28 2 + 8 = 10 1 + 0 = 1)

Let’s put this strategy to the test using the numbers 36573 and 21904.

## Perfect square formula

The perfect square formula is expressed as two terms, such as (a + b) * 2. (a + b)2 = a*2 + 2*ab + b*2 is the extension of the perfect square formula.

## List of perfect squares

0 = 0² = 0 * 0\newline 1 = 1² = 1 * 1\newline 4 = 2² = 2 * 2\newline 9 = 3² = 3 * 3\newline 16 = 4² = 4 * 4\newline 25 = 5² = 5 * 5\newline 36 = 6² = 6 * 6\newline 49 = 7² = 7 * 7\newline 64 = 8² = 8 * 8\newline 81 = 9² = 9 * 9\newline 100 = 10² = 10 * 10\newline 121 = 11² = 11 * 11\newline 144 = 12² = 12 * 12\newline 169 = 13² = 13 * 13\newline 196 = 14² = 14 * 14\newline 225 = 15² = 15 * 15\newline 256 = 16² = 16 * 16\newline 289 = 17² = 17 * 17\newline 324 = 18² = 18 * 18\newline 361 = 19² = 19 * 19\newline 400 = 20² = 20 * 20\newline 441 = 21² = 21 * 21\newline 484 = 22² = 22 * 22\newline 529 = 23² = 23 * 23\newline 576 = 24² = 24 * 24\newline 625 = 25² = 25 * 25\newline 676 = 26² = 26 * 26\newline 729 = 27² = 27 * 27\newline 784 = 28² = 28 * 28\newline 841 = 29² = 29 * 29\newline 900 = 30² = 30 * 30\newline 961 = 31² = 31 * 31\newline## Frequently Asked Questions

### Is 1 a perfect square?

Perfect numbers are **positive numbers** that may be represented as a number multiplied by itself, and the number generated by squaring a whole number will be a perfect square.

So, if we multiply 1 by 1, we get 1 as a whole number, so yes, 1 is a perfect square, and we get a perfect square anytime we multiply the number by itself.

### Is 125 a perfect square?

No, 125 does not form a perfect square. So why isn’t 125 a perfect square?

A perfect square is a number that is the product of two equal integers.

Finding the components is the only way to determine if a number is a perfect square. However, before we go to the difficulty of locating the variables, you can use a fast method to assist assess whether the extra work is even necessary.

### Perfect square definition

A **perfect square** is a number that may be written as the product of an integer by itself or as an integer’s second exponent. For example, 25 is a perfect square since it is the product of the integer 5 multiplied by itself, 5 * 5 = 25. However, because it cannot be written as the product of two equal integers, 21 is not a perfect square number.