How to Use the Square Root Table for Fast and Accurate Math Solutions
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 – Values, Chart & PDF
1. What is a square root table, and why is it useful for students?
A square root table is a chart that lists the square roots of whole numbers. It's a handy reference tool, especially for students, because it allows for quick lookups during exams and problem-solving. This saves valuable time and helps improve accuracy by avoiding lengthy manual calculations. The table is particularly useful for mental math practice and improving speed in competitive exams.
2. How do I use a square root table to find the square root of a number, for example, √25?
To find the square root of a number using a square root table, simply locate the number in the table's 'Number' column. The corresponding value in the 'Square Root' column is the answer. For example, to find √25, locate 25 in the Number column; the adjacent value in the Square Root column will be 5.
3. What is the difference between a square and a square root?
The square of a number is the result of multiplying the number by itself (e.g., 5² = 5 * 5 = 25). The square root is the inverse operation: it's a number that, when multiplied by itself, gives the original number (e.g., √25 = 5 because 5 * 5 = 25).
4. Are there any tricks to help me remember common square roots?
Yes! Memorizing the squares of small numbers (1-10) is a great start. You can use flashcards, practice problems, or even create visual aids to help you memorize these values. Also, recognizing patterns in the table can make memorization easier. For instance, notice how square roots of perfect squares are whole numbers.
5. What are perfect squares, and how can I identify them in the square root table?
A perfect square is a number that is the square of an integer (whole number). In a square root table, perfect squares are easily identified as they have whole number square roots (e.g., 1, 4, 9, 16, 25 are perfect squares, as their square roots are 1, 2, 3, 4, 5 respectively). Look for whole numbers in the 'Square Root' column to find them.
6. How accurate are the values in the square root table? Are they rounded?
The values in a square root table are usually approximate, often rounded to a certain number of decimal places (e.g., three decimal places). This is because many square roots are irrational numbers (numbers that cannot be expressed as a simple fraction), and their decimal representations go on infinitely.
7. Can I use this table for numbers larger than 50?
This particular table only covers numbers from 1 to 50. For numbers larger than 50, you would need a more extensive square root table or use a calculator.
8. How does the square root table help with problem-solving in mathematics?
The square root table significantly speeds up problem-solving, particularly in areas involving geometry (calculating areas or volumes), trigonometry, and physics where square roots are frequently needed. It reduces calculation errors and allows students to focus on applying mathematical concepts instead of getting bogged down in arithmetic.
9. Is there a downloadable version of this square root table?
Yes, a downloadable PDF version of the square root table (1-50) is available for convenience. [Insert Link to PDF Here]
10. What are some common mistakes students make when using square root tables?
Common mistakes include misreading the table (incorrectly matching numbers and their roots), failing to consider the context of the problem (units, significant figures), and not understanding the approximation inherent in the table. Careful attention to detail is key.
11. How can I improve my speed and accuracy in finding square roots?
Regular practice using the table is vital. Try solving timed practice problems that require looking up square roots. Also, memorize the roots of common numbers to further improve your speed. Combining table use with mental math strategies will boost your overall efficiency.
12. Beyond exams, where else might I use a square root table or the concept of square roots?
Square roots have widespread applications in various fields. These include: engineering (structural calculations), computer science (algorithms), physics (calculating speed and velocity), and finance (compound interest formulas).
