# Squares 1 to 100

Squares play an important role in various fields of study, especially mathematics. To quickly solve mathematical issues, you must be able to recall squares. The Squares from 1 to 100 will be covered in this article along with the concept to determine them. ## What is a Square?

The result of multiplying a number with that same number is known as the square of the original number. For example, to calculate the square of X, we need to multiply X by X itself, i.e., X x (multiplication sign) X or X^2.

Example:

• A square of 2 is 2 × 2 = 4
• A square of 3 is 3 × 3 = 9
• A square of 4 is 4 × 4 = 16
• A square of 5 is 5 × 5 = 25
• A square of 6 is 6 × 6 = 36, and so on.

## Squares from 1 to 100

The square of 1 to 100 can be written in exponential notation as (X)^2, where x represents values starting from 1 and going up to 100

• Form of Exponent: (x)^2
• Maximum Value: 100^2 equals 10,000.
• Minimum Value: 1^2 = 1.

Squares from 1 to 100:

Let's read the squares below, which range from 1 to 100:

 12 = 1 212 = 441 412 = 1681 612 = 3721 812 = 6561 22 = 4 222 = 484 422 = 1764 622 = 3844 822 = 6724 32 = 9 232 = 529 432 = 1849 632 = 3969 832 = 6889 42 = 16 242 = 576 442 = 1936 642 = 4096 842 = 7056 52 = 25 252 = 625 452 = 2025 652 = 4225 852 = 7225 62 = 36 262 = 676 462 = 2116 662 = 4356 862 = 7396 72 = 49 272 = 729 472 = 2209 672 = 4489 872 = 7569 82 = 64 282 = 784 482 = 2304 682 = 4624 882 = 7744 92 = 81 292 = 841 492 = 2401 692 = 4761 892 = 7921 102 = 100 302 = 900 502 = 2500 702 = 4900 902 = 8100 112 = 121 312 = 961 512 = 2601 712 = 5041 912 = 8281 122 = 144 322 = 1024 522 = 2704 722 = 5184 922 = 8484 132 = 169 332 = 1089 532 = 2809 732 = 5329 932 = 8649 142 = 196 342 = 1156 542 = 2916 742 = 5476 942 = 8836 152 = 225 352 = 1225 552 = 3025 752 = 5625 952 = 9025 162 = 256 362 = 1296 562 = 3136 762 = 5776 962 = 9216 172 = 289 372 = 1369 572 = 3249 772 = 5929 972 = 9409 182 = 324 382 = 1444 582 = 3364 782 = 6084 982 = 9604 192 = 361 392 = 1521 592 = 3481 792 = 6241 992 = 9801 202 = 400 402 = 1600 602 = 3600 802 = 6400 1002 = 10000

## What characteristics do square numbers have?

The following characteristics of square numbers can be generalized based on what we saw in the previous section on the list of squares from 1 to 100:

• Square numbers (results) typically have a unit place ending with 0 (especially an even number of zeros or 00), 1, 4, 5, 6, or 9.
• A number's square result value will always have a 1 at the end in case the original number ends with 1 or 9.
• A number's square result value will always have a 6 at the end in case the original number ends with 4 or 6.
• A number ending with a double zero (or with an even number of zeros/ 00) will be a perfect square.
• A number ending in 2, 3, 7 or 8 cannot be a perfect square.
• A perfect square's square root value is always a natural integer.

## How to determine the values of Squares from 1 to 100?

We may use any of the following approaches to compute the squares from 1 to 100:

### Approach 1: Simple Multiplication

By multiplying the number by itself, we may obtain the square of the original number, be it small or large. For example, using this technique, we can determine that square of 8 (i.e., 8x8) equals 64. In other words, the final value or resultant value "64" is the square of the value "8". For lesser (or small) numbers, this strategy works effectively.

### Approach 2: Applying Fundamental Algebraic Identities

This method is often used to simplify large values and then find their squares. To find the square of 49, for instance, we can write 49 as follows:

• Choice A is (40 + 9)^2
• Choice B is (50 - 1)^2

The fundamental algebraic identity formula (a±b)^2 = (a2+b2±2ab) is used in the next step to obtain the following results:

• Choice A, [402 + 92+ (2×40 × 9)], and
• Choice B, [502 + 12- (2×50 × 1)].

It is clear that 'a' represents the value '40' and 'b' represents the value '9' for choice A, whereas in choice B, 'a' represents the value '50' and ' b' represents the value '1'. Therefore, we get the following results:

• Choice A: (1600 + 81 + 720) = 2401, and
• Choice B: (2500 + 1 - 100) = 2401

We can see that the value of 2401 is the result of both the choices (equations) used to find the value of square 49.

## Example: Use of Squares in Real Life

Question: There is a round tabletop with a radius of 50 inches. What will be the area of that tabletop? [Use π = 3.14]

Solution:
As we know that the area of a circle is πr^2, where r is the radius.
Therefore, Area of tabletop = π(50)2

Using the square values from 1 to 100 chart, 502 = 2500.
So, the Area of the tabletop = 2500π
Since the value of π is 3.14, the Area of the tabletop = 2500 × 3.14 = 7850
Hence, the tabletop's area is 7850 inches2.

## The Bottom Line

As an outcome, investigating the idea of squares from 1 to 100 shows remarkable patterns and insights into the field of mathematics. The total number of perfect square numbers in this range, 10, has led us to the conclusion that perfect squares are widely distributed within numbers. These squares reveal an unusual arrangement, whether represented in a square grid or when visualized on a number line, in addition to having distinctive characteristics, such as being the result of a number multiplied by itself. In addition, a study of squares reveals relationships with a number of mathematical ideas, including factors, divisibility, and even geometry. Overall, the study of squares from 1 to 100 is an excellent illustration of the variety and beauty of mathematics and how it has significantly influenced how we see the world.

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