1 to 100 Squares

Squares are an important part of mathematics. A square of a number means multiplying the number by itself.
For example:
2² = 2 × 2 = 4
5² = 5 × 5 = 25

In this post, we will see the squares of numbers from 1 to 100.

What is a Square?
The square of a number means multiplying the number by itself.
In short, Square of a number = Number × Number.
Example:

• Square of 2 = 2 × 2 = 4
• Square of 7 = 7 × 7 = 49

List of Squares from 1 to 100:

Download the PDF of 1 to 100 Squares from the link given below.

Why Should You Learn Squares from 1 to 100?

• Fast Calculation: Helps in fast mental math.
• Exam Preparation: Important for competitive exams like SSC, Banking, Railway, etc.
• Algebra: Helps in solving equations and formulas quickly.
• Confidence: Knowing squares improves your overall confidence in mathematics.

Tips to Learn Squares Easily

• Practice daily: Repetition will make you fast.
• Group the numbers: Learn squares of 1–10 first, then 11–20, and so on.
• Notice patterns: Notice the patterns in squares. For example, squares of numbers ending with 5 always end in 25 (like 15² = 225, 25² = 625).
• Use tricks: Some shortcut tricks can help you find squares quickly.
• Write and revise: Write squares regularly to improve memory.

Short Tricks to Remember Squares Quickly

1. Numbers Ending with 5
If a number ends with 5, you can find its square easily.
👉 Trick: Multiply the first digit(s) by the next number, then add 25 at the end.

• Example:
  • 25² → (2 × 3) = 6 → So, 625
  • 45² → (4 × 5) = 20 → So, 2025
  • 65² → (6 × 7) = 42 → So, 4225

2. Square of Numbers Near 50
If a number is close to 50, use this trick.
👉 Trick: Formula = (50 + x)² = 2500 + (x × 100) + (x²)

• Example:
  • 52² → (50 + 2)²
    • → 2500 + (2 × 100) + (2²)
    • → 2500 + 200 + 4 = 2704
  • 48² → (50 – 2)²
    • → 2500 – (2 × 100) + (2²)
    • → 2500 – 200 + 4 = 2304

3. Square of Numbers Ending with 1
👉 Trick: (n)² = (n-1)(n+1) + 1

• Example:
  • 11² → (10 × 12) + 1 = 121
  • 21² → (20 × 22) + 1 = 441

4. Multiply and Double Method
If you know a small square, use this to find nearby squares.
👉 Trick: (n+1)² = n² + (2n + 1)

• Example:
  • 13² → 169
  • 14² → 13² + (2×13) + 1 = 169 + 26 + 1 = 196

5. Perfect Square Pattern
👉 Notice the pattern: Squares of even numbers and odd numbers create simple sequences.

• Example:
  • 1² = 1
  • 3² = 9
  • 5² = 25
  • 7² = 49
  • 9² = 81

👉 The difference between these squares is increasing by 8 every time (8, 16, 24, 32…).

6. Square Numbers End with Specific Digits
Square numbers can end in 0, 1, 4, 5, 6, or 9 but never 2, 3, 7, or 8.

Tricks to Remember Squares

👉Trick 1: Memorize Important Squares
Memorize squares of 1–30 at least. These are used very often.

👉Trick 2: Memorize in Sets
Learn 1–10 first.
Then 11–20, and so on.

👉Trick 3: Break Big Numbers (Use Algebra)
(a+b)² = a² + 2ab + b²
For example,
42² = (40 + 2)²
= 40² + 2×40×2 + 2²
= 1600 + 160 + 4 = 1764

👉Trick 4: Visual Method
Imagine square numbers as areas of squares (length × breadth).

👉Trick 5: Smart Practice
Use flashcards.
Practice 5–10 minutes daily.

Uses of Squares in Real Life

• Area Calculation: Area of a square = side × side.
• Speed and Distance: In physics, formulas often involve squares.
• Banking: Calculating interest rates involves squares sometimes.
• Technology: Computer graphics use squares in pixel calculations.

Final Tips

• Practice Daily: Spend 5–10 minutes daily.
• Group numbers: Group numbers and learn in sets.
• Use Flashcards: Write the number on one side and its square on the other.
• Challenge Yourself: Try to say squares of random numbers in 10 seconds.

Conclusion

Learning squares from 1 to 100 helps you in math exams, competitive exams, and everyday calculations. Practice a little every day, and soon you will remember all the squares easily!

Some Important Links
Download 1 to 100 Squares PDF	Click Here

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