Complete Square Root Table From 1 to 50 with Step by Step Usage Guide
The concept of Square Root Table From 1 to 50 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Having a ready-reference table for square roots not only saves time but also helps students avoid calculation errors and boost their mental-math skills during practice and competitive tests.
What Is Square Root Table From 1 to 50?
A square root table from 1 to 50 is a handy chart listing the principal (positive) square root values (√n) for every integer from 1 to 50, calculated up to 3 or 4 decimals. You’ll find this concept applied in square root calculations, estimation techniques, and mental arithmetic during exams.
Key Formula for Square Root
Here’s the standard formula: \( \sqrt{n} \), where n is any positive integer. For perfect squares (like 4, 9, 25), the result is an exact positive integer. For others, the value is a non-terminating decimal.
Square Root Table from 1 to 50 (Printable & Fast Reference)
The square root table from 1 to 50 lists values of √n for numbers 1 to 50. This table lets you find roots instantly—helpful for exams, practice, and quick calculations.
| Number (n) | √n | Number (n) | √n | Number (n) | √n | Number (n) | √n |
|---|---|---|---|---|---|---|---|
| 1 | 1.000 | 13 | 3.606 | 25 | 5.000 | 37 | 6.083 |
| 2 | 1.414 | 14 | 3.742 | 26 | 5.099 | 38 | 6.164 |
| 3 | 1.732 | 15 | 3.873 | 27 | 5.196 | 39 | 6.245 |
| 4 | 2.000 | 16 | 4.000 | 28 | 5.292 | 40 | 6.325 |
| 5 | 2.236 | 17 | 4.123 | 29 | 5.385 | 41 | 6.403 |
| 6 | 2.449 | 18 | 4.243 | 30 | 5.477 | 42 | 6.481 |
| 7 | 2.646 | 19 | 4.359 | 31 | 5.568 | 43 | 6.557 |
| 8 | 2.828 | 20 | 4.472 | 32 | 5.657 | 44 | 6.633 |
| 9 | 3.000 | 21 | 4.583 | 33 | 5.745 | 45 | 6.708 |
| 10 | 3.162 | 22 | 4.690 | 34 | 5.831 | 46 | 6.782 |
| 11 | 3.317 | 23 | 4.796 | 35 | 5.916 | 47 | 6.856 |
| 12 | 3.464 | 24 | 4.899 | 36 | 6.000 | 48 | 6.928 |
| 49 | 7.000 | 50 | 7.071 |
Downloadable Table: Click here for square root table (PDF).
How to Use the Table?
- Find your number (n) in the first column.
- Read the value in the “√n” column right next to it.
- Use that root value in place of long calculations while solving a problem or checking your answer.
- If your number is not listed, locate the closest smaller and higher numbers and estimate between their roots for a quick approximation.
For example, to find √48: Table shows 6.928. So, √48 ≈ 6.928 for most quick calculations.
Square Numbers vs Square Roots (Know the Difference!)
A square number is the result of multiplying a number by itself (like 16 = 4 × 4). The square root is the value you must square to get that number (like √16 = 4). Between 1 and 50, the perfect squares are:
- 1 (√1 = 1)
- 4 (√4 = 2)
- 9 (√9 = 3)
- 16 (√16 = 4)
- 25 (√25 = 5)
- 36 (√36 = 6)
- 49 (√49 = 7)
Benefits of Memorizing Common Roots
- Speeds up calculations in exams and quizzes.
- Reduces errors caused by manual root-finding.
- Helps with faster mental math (great for Olympiads, JEE, NTSE, NEET, and Board exams).
- Makes tricky word problems and geometry easier to solve.
- Works even when a calculator isn’t allowed.
Vedantu students often use this chart when practicing square root questions and math tricks for quick problem-solving.
Try These Yourself
- What is the square root of 36?
- Find the square roots of 15, 27, and 33 using the table.
- Which numbers between 1 and 50 are perfect squares?
- Estimate the square root of 44 by referencing two closest values in the table.
Frequent Errors and Misunderstandings
- Confusing square numbers (like 25) with their roots (like 5).
- Assuming all roots are whole numbers—most are NOT.
- Relying only on calculators—tables help with estimation and mental math speed.
Relation to Other Maths Concepts
Knowing how to use the square root table from 1 to 50 also helps you solve square numbers, cube roots, and root problems by prime factorization quickly. Mastering this builds confidence for all advanced maths concepts.
Classroom Tip
A good way to remember common square roots (like √2 ≈ 1.414, √3 ≈ 1.732) is to write them on small sticky notes or use flashcards. Vedantu’s teachers encourage regular quick practice with these tables so students can instantly recall values during assessments.
We explored Square Root Table From 1 to 50 — from its definition, usage, sample problems, and powerful exam shortcuts. Continue practicing with Vedantu to become quick and confident in solving root problems for school and competitive exams.
Related Internal Links for Practice & Deeper Learning
- Square Root – Foundational concepts and calculation methods
- Square Numbers for Kids – Easy-to-understand visuals of perfect squares
- Square Root Tricks – Fast tricks, memory aids for square root calculations
- Square Root Finder – Online tool to calculate roots for any number
FAQs on Square Root Table From 1 to 50 with Accurate Values
1. What is the square root table from 1 to 50?
The square root table from 1 to 50 lists the values of √n for numbers between 1 and 50. It helps students quickly find approximate decimal values of square roots without calculation.
- √1 = 1
- √4 = 2
- √9 = 3
- √16 = 4
- √25 = 5
- √36 = 6
- √49 = 7
2. How do you find the square root of numbers from 1 to 50?
You can find the square root of numbers from 1 to 50 using prime factorization, long division method, or a calculator. For perfect squares, identify a number that multiplies by itself to give the original number.
- Example: 36 = 6 × 6, so √36 = 6
3. Which numbers between 1 and 50 are perfect squares?
The perfect squares between 1 and 50 are numbers whose square roots are whole numbers. These are:
- 1 (1²)
- 4 (2²)
- 9 (3²)
- 16 (4²)
- 25 (5²)
- 36 (6²)
- 49 (7²)
4. What is the value of √50?
The value of √50 is approximately 7.071. It can be simplified as √50 = √(25 × 2) = 5√2, and since √2 ≈ 1.414, multiplying gives 5 × 1.414 ≈ 7.071.
5. Why is a square root table from 1 to 50 important?
A square root table from 1 to 50 is important because it helps students quickly reference square root values for calculations and problem-solving. It is useful in:
- Simplifying surds
- Solving quadratic equations
- Geometry problems (area and Pythagoras theorem)
- Competitive exam preparation
6. How do you simplify square roots between 1 and 50?
You simplify a square root by factoring out the largest perfect square from the number. For example:
- √18 = √(9 × 2)
- = √9 × √2
- = 3√2
7. Are square roots from 1 to 50 rational or irrational?
Square roots of perfect squares are rational numbers, while others are irrational numbers. For example:
- √16 = 4 (rational)
- √25 = 5 (rational)
- √2 ≈ 1.414... (irrational)
- √7 ≈ 2.646... (irrational)
8. What is the square root of 20?
The square root of 20 is approximately 4.472. It can be simplified as √20 = √(4 × 5) = 2√5, and since √5 ≈ 2.236, multiplying gives 2 × 2.236 ≈ 4.472.
9. How can students memorize the square root table from 1 to 50 easily?
Students can memorize the square root table from 1 to 50 by focusing first on perfect squares and common simplified surds. Effective tips include:
- Memorize squares from 1² to 7²
- Practice writing square roots daily
- Learn common approximations like √2 ≈ 1.414
- Use flashcards and quizzes
10. What is the difference between a perfect square and a non-perfect square?
A perfect square has a whole number as its square root, while a non-perfect square has an irrational square root. For example:
- 36 is a perfect square because √36 = 6
- 30 is a non-perfect square because √30 ≈ 5.477
