# Perfect Square List 1 to 1000: Understanding the Numbers that Square Up

## What is a Perfect Square?

What exactly is a perfect square?

A number multiplied by itself makes a perfect square. That is any whole number can be squared to create a number that is called a perfect square.

For example 9 is a perfect square because its product is produced by multiplying the number by itself; 9 = 3 x 3.

This blog will explain the idea of perfect squares and teach you how to spot them. You will understand the formula of a perfect square, its applications, properties, list of perfect squares, and a few solved examples.

## Perfect Square List 1 to 100

There are a total number of ten perfect squares between 1 and 100 which are 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100.

## Perfect Square List 101 to 200

There are a total number of four perfect squares between 101 and 200 which are 121 , 144, 169, 196.

## Perfect Square List 201 to 300

There are a total number of three perfect squares between 201 and 300 which are 225, 256, 289.

## Perfect Square List 301 to 400

There are a total number of three perfect squares between 301 and 400 which are 324, 361, 400.

## Perfect Square List 401 to 500

There are a total number of two perfect squares between 401 and 500 which are 441 and 484.

## Perfect Square List 501 to 600

There are a total number of two perfect squares between 501 and 600 which are 529 and 576.

## Perfect Square List 601 to 700

There are a total number of two perfect squares between 601 and 700 which are 625 and 676.

## Perfect Square List 701 to 800

There are a total number of two perfect squares between 701 and 800 which are 729 and 784.

## Perfect Square List 801 to 900

There are a total number of two perfect squares between 801 and 900 which are 841 and 900.

## Perfect Square List 901 to 1000

There is only one perfect square between 901 and 1000 which is 961.

## Perfect Square Formula

Assume that y is the product of x and x =x², if x is a whole number and y is a perfect square of x.

Consequently, the perfect square formula is written as y =x²

Perfect Square Formula

Now let’s replace the formula with values.

If y = x² and x = 4, then. Accordingly,

y = 4 × 4 = 16.

Given that it is the square of the whole number 4, is 16 in this case, which is a perfect square.

## How to Find the Perfect Square of a Number?

The first step is to observe that

1. The final number in every perfect square is either 1, 4, 5, 6, 9 or 00.

Now, do the following tests after removing the zeros from all integers that finish in 1, 4, 5, 6, and 9, as well as any numbers that end in even zeros:

2. Digital roots are available in 1, 4, 7, and 9. Unless its digital root is one of the following: 1, 4, 7, or 9, a number cannot be a perfect square. (To determine a number’s digital root, sum all of its digits. Add the digits of this amount if it is greater than 9. The number’s digital root is the single digit that can be found at the end.)

3. If the unit digit is 5, the tenth digit will always be 2.

4. Unless the number ends in 6, the tenth digit is always even (1, 3, 5, 7, and 9). That means the tenth digit is always even if it ends in 1, 4, or 9. (2, 4, 6, 8, 0).

5. When a number is divided by 8 and its square is divisible by 4, it has a 0 as the final result.

6. When an even number is squared and not divisible by 4, it always leaves a remnant of 4, yet when an odd number is squared and divisible by 8, it always leaves a remainder of 1.

7. A perfect square’s total number of prime factors is always odd.

## What are the Properties of a Perfect Square?

1. Square numbers have a unit place ending in 0, 1, 4, 5, 6, or 9.

Example:

1² = 1

2² = 4

3² = 9

4² = 16

2. If a number ends with 1 or 9, then its square will always end with 1.

Example:

19² = 361

21² – 441

3. The square of a number that ends in 4 or 6 will always end in 6.

Example:

14² = 196

16² – 256

4. A perfect square’s square root is always a natural number.

Example:

√16 = 4

√25 = 5

5. Even numbers of zeros will conclude the perfect squares.

Example:

10² = 100

20² – 400

6. Squares of even numbers are always even.

Example:

6² = 36

12² – 144

7. The square of an odd number is always odd.

Example:

7² = 49

15² – 225

8. The unit digit of a number’s square matches the unit digit of its last digit.

This feature states that a two-digit number, for instance, will have the same digit at the unit place in its square as it will in the square of its unit digit.

Example:

23² = 529

There are 3 in the unit place of 23 and 9 in the unit place of 529.

9 is equivalent to the square of 3

#### FAQ's on Perfect Square List 1 to 1000

1 is a perfect square since 1 x 1 equals 1 itself when multiplied by 1.

Zero is regarded as a perfect square because it fits all of the criteria for squares.

0 x 0 = 0

Yes, 100 is a perfect square as 10 x 10 = 100.

The final number in every perfect square is either 1, 4, 5, 6, 9 or 00.