# Perfect Square Calculator

Created by Łucja Zaborowska, MD, PhD candidate
Reviewed by Steven Wooding
Last updated: Nov 23, 2022

Looking for the perfect square calculator? Check our easy tool and quickly find out whether your number belongs to the noble list of perfect squares. 🖼️

Check out our article below to discover the definition of the perfect square, a full list of perfect square numbers from 0 to 1000, and a few easy steps on calculating that all.

## What is a perfect square number?

A perfect square number is a number that can be created by multiplying two identical integers; in other words, the perfect square's root is a whole number.

💡 Integer is a name for a whole number that can be either negative, positive or equal to 0. Integer cannot contain fractions or decimals.

• Examples of integers: -5, 0, 3, 235.
• Examples of numbers that are not integers: 1.2, 3¾, 0.25.

Looking for a different type of complete the perfect square calculator? We can also distinguish a perfect square trinomial, given in a form of ax² + bx + c. This particular formula should also satisfy the b² = 4ac condition.

We talked about the squares, now it's time to think about the roots in math - check our universal root calculator or the cube root tool. 🥕

## How to use the perfect square calculator?

This section will teach you how to use the perfect square calculator - with steps!

You may enter any number you want, of any desired value and length (well, up to a point). Don't hesitate to enter whole equations; go ahead and try multiplication (5*67), division (3/675), addition (1+1), or subtraction (1.56-0.86).

Your result will not only include a simple message about your number being a perfect square or not - our complete the square calc will also display a simple, step-by-step explanation.

The perfect square is too easy for you? Try something from the advanced level 🔬 such as our complex root calculator, or root mean square calculator.

## How to calculate a perfect square?

To check the perfectness of your square, you can simply calculate the square root of a given number. If the square root is an integer, your number is the perfect square.

Let's calculate the squares of the following numbers: 49 and 53.

√49 = 7 - 7 is an integer → number 49 is a perfect square.

√53 = 7.280109 - 7.280109 is not an integer → number 53 isn't a perfect square.

What if you don't have a calculator, and your number's quite big?

Let's try a more exciting method:

1. It's good to know that all perfect squares end with 1, 4, 5, 6, 9, or 00. That's how you can perform a quick first selection and decide which number can and cannot be a perfect square.

• If your number ends with 1, 4 or 9, its ten's digit should always be even (0, 2, 4, 6, 8) for it to be the perfect square.
• If your number ends with 5, its ten’s digit is always 2.
• If your number ends with 6, its ten’s digit is always odd (1, 3, 5, 7, and 9)
2. We also need to be aware that the digital root of the number must be equal to 0, 1, 4, or 7. If the calculated digital root is not one of the mentioned values, your number cannot be a perfect square.

💡 We can easily calculate the digital root of a number by adding all digits in the number, and then, if the obtained sum has two digits, sum them as well. (E.g., 1234567 → 1+2+3+4+5+6+7 = 28 → 2 + 8 = 10 → 1 + 0 = 1) .

Let's try out this method using the two following numbers: 36573 and 21904.

### 1st example: 36576

1. Does the number end with 1, 4, 5, 6, 9, or 00?

Yes, our number might be a perfect square.

2. Our number ends with 6 - is its ten's digit an odd number?

Yes, its ten's digit is 7. Our number might be a perfect square.

3. What's the digital root of our number?

36573 = 3+6+5+7+3 = 24 = 2+4 = 6

The digital root of our number is not equal to 0, 1, 4, or 7. Our number cannot be a perfect square.

### 2nd example: 21904

1. Does the number ends with 1, 4, 5, 6, 9, or 00?

Yes, our number might be a perfect square.

2. Our number ends with 4 - is its ten's digit an even number?

Yes, its ten's digit is 0. Our number might be a perfect square.

3. What's the digital root of our number?

21904 = 2+1+9+0+4 = 16 = 1+6 = 7

Our number's digital root is equal to one of the following numbers: 0, 1, 4, or 7. So it's probably a perfect square.

## List of perfect squares

In the table below, you'll find all the squares that you're looking for; we list all the perfect squares from 0 to 1000.

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