Table of contents

What is a perfect square number?How to use the perfect square calculator?How to calculate a perfect square?List of perfect squaresFAQs* 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!

**Your input**See AlsoSquare Root CalculatorSquaring numbers (article) | Khan AcademySquare Root CalculatorArea of a Square. CalculatorYou 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**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:

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)

- If your number ends with
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. (For example, 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**

**Does the number end with 1, 4, 5, 6, 9, or 00?**Yes, our number might be a perfect square.

**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.

**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

be a perfect square.**cannot**

### 2nd example: **21904**

**Does the number ends with 1, 4, 5, 6, 9, or 00?**Yes, our number might be a perfect square.

**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.

**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 |

### How do I check to see if a number is a perfect square?

To figure out if a number is a perfect square, follow these steps:

- Get the number.
- Find the
**square root**of the number. - Check to see if the answer is an
**integer**(whole number). If it is, the original number is a perfect square.

### What is the square if the root is 6?

**The square is 36.** To find this answer, we find the square of the root:

**6 ^{2} = 36**

So, **36** is the perfect square of root **6**.

### Is 0 a perfect square?

A perfect square is created when we multiply an integer by itself.

`0 × 0 = 0`

As such, zero is considered a perfect square. `0`

and `1`

are unusual in that they are the only two integers where the roots and squares are the same.

### Are perfect squares rational or irrational numbers?

**All square numbers are rational numbers.**

A rational number is a number that can be expressed as a fraction where both the numerator and denominator are integers, and the denominator is greater than 0. All positive numbers (of which square numbers are a subset) can be expressed as fractions. Irrational numbers, on the other hand, cannot be written as fractions.

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