How to Learn and Remember Squares 1 to 30 Easily for Exams
The concept of square 1 to 20 is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Knowing the squares of numbers from 1 to 20 allows for quick mental calculations, simplification of expressions, and fast problem-solving skills, especially in school board and competitive exams.
Understanding Square 1 to 20
A square 1 to 20 refers to the series of perfect squares for numbers starting from 1 and ending at 20. In simple terms, the square of a number is the result you get when you multiply the number by itself. For example, the square of 7 is \( 7 \times 7 = 49 \). Understanding these squares helps in areas such as algebra, square roots, and patterns in number sequences.
Formula Used in Square 1 to 20
The standard formula to find the square of a number \( n \) is: \( n^2 = n \times n \)
Here’s a helpful table to understand square 1 to 20 more clearly:
Square 1 to 20 Table
| Number | Square | Square in Words |
|---|---|---|
| 1 | 1 | One squared is one |
| 2 | 4 | Two squared is four |
| 3 | 9 | Three squared is nine |
| 4 | 16 | Four squared is sixteen |
| 5 | 25 | Five squared is twenty-five |
| 6 | 36 | Six squared is thirty-six |
| 7 | 49 | Seven squared is forty-nine |
| 8 | 64 | Eight squared is sixty-four |
| 9 | 81 | Nine squared is eighty-one |
| 10 | 100 | Ten squared is one hundred |
| 11 | 121 | Eleven squared is one hundred twenty-one |
| 12 | 144 | Twelve squared is one hundred forty-four |
| 13 | 169 | Thirteen squared is one hundred sixty-nine |
| 14 | 196 | Fourteen squared is one hundred ninety-six |
| 15 | 225 | Fifteen squared is two hundred twenty-five |
| 16 | 256 | Sixteen squared is two hundred fifty-six |
| 17 | 289 | Seventeen squared is two hundred eighty-nine |
| 18 | 324 | Eighteen squared is three hundred twenty-four |
| 19 | 361 | Nineteen squared is three hundred sixty-one |
| 20 | 400 | Twenty squared is four hundred |
This table makes it easy to revise or memorize the square values of numbers from 1 to 20—essential for speedy maths calculations and mental maths practice.
Worked Example – Solving a Problem
Let’s solve a real exam-style question using the concept of square 1 to 20:
1. Find the area of a square whose side is 14 cm.Step 2. Substitute the value: Area = 14 × 14
Step 3. Find the square of 14 (from the table): 14 × 14 = 196
Step 4. So, the area is 196 cm².
2. Calculate the sum of the squares of 5 and 12.
Step 2. Find 12 squared = 144 (from the table)
Step 3. Add both squares: 25 + 144 = 169
Practice Problems
- What is the square of 9?
- Write the squares of numbers 16 to 20.
- Is 225 a square number between 1 and 20?
- List all even numbers from 1 to 20 whose squares end with 6.
- Find the square of 15 in words.
Common Mistakes to Avoid
- Confusing square 1 to 20 with multiplying by 2 instead of itself.
- Using squares for odd numbers but forgetting even numbers (or vice versa).
- Forgetting to use the correct square value in formulas during exams.
Real-World Applications
The concept of square 1 to 20 is very practical. It appears in finding areas of squares, calculating distance, working with patterns in science, and even in finance. At Vedantu, teachers show how mastering these squares helps students answer questions faster and build a strong foundation for advanced maths like square roots and quadratic equations.
We explored the idea of square 1 to 20, its table, formula, common mistakes, and applications. Practice regularly and use Vedantu resources to master squares and speed up your maths skills.
Useful Internal Links for More Learning
- Squares and Square Roots – Concepts and Tricks
- Square Roots from 1 to 25 Table
- Multiplication Tables from 1 to 20
- Table of 10
- Table of 12
- Square Root Table from 1 to 50
- Square Root of 4
- Square Root of 9
- Square Root of 5
- Square Root of 20
FAQs on Squares from 1 to 20 with Full Table and Quick Learning Guide
1. What are the squares of numbers from 1 to 20?
Squares from 1 to 20 are the result of multiplying a number by itself. Here they are:
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
11² = 121
12² = 144
13² = 169
14² = 196
15² = 225
16² = 256
17² = 289
18² = 324
19² = 361
20² = 400
2. What are the cubes of numbers from 1 to 20?
Cubes from 1 to 20 are calculated by multiplying a number by itself twice. Here is the list:
1³ = 1
2³ = 8
3³ = 27
4³ = 64
5³ = 125
6³ = 216
7³ = 343
8³ = 512
9³ = 729
10³ = 1000
11³ = 1331
12³ = 1728
13³ = 2197
14³ = 2744
15³ = 3375
16³ = 4096
17³ = 4913
18³ = 5832
19³ = 6859
20³ = 8000
3. What is the square of numbers from 1 to 100?
Squares from 1 to 100 are found by multiplying each number by itself. For example, 1² = 1, 2² = 4, ... up to 100² = 10,000. You can check a full square table or refer to worksheets for all values.
4. How do you write the square roots from 1 to 20?
Square root of a number is the value that, when multiplied by itself, gives the original number. The square roots from 1 to 20 are:
√1=1
√2=1.414
√3=1.732
√4=2
√5=2.236
√6=2.449
√7=2.646
√8=2.828
√9=3
√10=3.162
√11=3.317
√12=3.464
√13=3.606
√14=3.742
√15=3.872
√16=4
√17=4.123
√18=4.243
√19=4.359
√20=4.472
5. What is the best way to learn squares from 1 to 30 easily?
To memorize squares 1 to 30 easily:
- Group numbers: Memorize in sets like 1–5, 6–10, etc.
- Look for patterns: Odd square differences increase by 2; e.g., 3²–2²=5, 4²–3²=7.
- Practice regularly with tables or worksheets.
- Use flashcards or quiz apps to test yourself.
6. What are the cubes of numbers from 1 to 30?
Cubes from 1 to 30 include: 1³=1, 2³=8, 3³=27, up to 30³=27,000. Memorizing the cubes helps with higher math problems and competitive exams.
7. What are the square roots from 1 to 100?
Square roots from 1 to 100 include both perfect and non-perfect squares. For example, √1=1, √4=2, √9=3, √16=4, and so on up to √100=10. For non-perfect squares, use approximations (e.g., √2 ≈ 1.41).
8. How can I download square and cube tables (PDF) for 1 to 200?
Square and cube tables from 1 to 200 in PDF format are often available on educational websites. Search for 'Square 1 to 200 PDF' or 'Cube 1 to 200 worksheets PDF' to find downloadable resources for practice and revision.
9. How can I use square and cube tables for quizzes and exams?
Square and cube tables help in quick calculations for MCQs, Olympiads, and competitive exams. Regular practice improves mental math and boosts speed in solving questions that involve squares, cubes, and their roots.
10. What are the squares from 1 to 25?
Squares from 1 to 25 are as follows: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625.
11. What is the cube root of numbers from 1 to 20?
Cube roots from 1 to 20 are values that, when multiplied by themselves twice, equal the original number. For example, the cube root of 8 is 2, because 2 × 2 × 2 = 8. Some cube roots are irrational; for example, ∛2 ≈ 1.26, ∛3 ≈ 1.44, ∛5 ≈ 1.71.
12. What is the square of 20?
Square of 20 is calculated as 20 × 20 = 400.
