Square Roots from 1 to 100: Chart, List & Shortcuts

The Square Root 1 to 100 is a core concept in mathematics, especially useful for quick calculation, mental math, and problem-solving in school and competitive exams. Mastering the square roots of numbers from 1 to 100 helps students solve a variety of arithmetic and algebra questions efficiently. Building this knowledge also strengthens number sense and speed in exams.

Understanding Square Roots 1 to 100

A square root of a number is a value that, when multiplied by itself, gives the original number. In mathematics, the square root is denoted by the radical symbol √. For example, √9 = 3 because 3 × 3 = 9. Knowing the square roots from 1 to 100 is essential because these values are often used in calculations involving area, algebra, and geometry. Practicing with a square root table can help with fast recall.

Square Roots Table from 1 to 100

Below is a comprehensive table of numbers from 1 to 100, their squares, and square roots. Perfect squares are marked for easy identification. This table helps you memorize and quickly look up any square root value up to 100.

Perfect Squares from 1 to 100

A perfect square is a number whose square root is a whole number. Here are the perfect squares between 1 and 100:

• 1 (√1 = 1)
• 4 (√4 = 2)
• 9 (√9 = 3)
• 16 (√16 = 4)
• 25 (√25 = 5)
• 36 (√36 = 6)
• 49 (√49 = 7)
• 64 (√64 = 8)
• 81 (√81 = 9)
• 100 (√100 = 10)

How to Find or Estimate Square Roots (Manual and Tricks)

There are several ways to find the square roots of numbers between 1 and 100:

• For perfect squares: Simply know or memorize their roots (e.g., √36 = 6).
• For non-perfect squares:
  1. Find the two nearest perfect squares it lies between. For example, for 70: 64 < 70 < 81.
  2. Estimate the root: √64 = 8, √81 = 9, so √70 is slightly above 8 (it is approximately 8.366).
  3. You can use prime factorization when possible. If not, use division or the average method for better accuracy.
• Tip: Practice estimation for fast mental math during exams.

For detailed steps, visit Square Root Long Division Method or Square Root Tricks & Shortcuts at Vedantu.

Worked Examples

Let's try out a few sample problems involving square roots:

1. Find the square root of 36.

   • Since 36 is a perfect square, √36 = 6.

2. Estimate the square root of 70.

   • √70 is between √64 (8) and √81 (9).
   • Since 70 is closer to 64, we can estimate √70 to be about 8.4. (Actual value: 8.366)

3. If x√100 = 2000, find x.

   • √100 = 10, so x × 10 = 2000 → x = 2000/10 = 200.

4. Evaluate 2 × √49.

   • √49 = 7, so 2 × 7 = 14.

Practice Problems

• List all perfect squares between 1 and 100.
• Find the square root of 81.
• Estimate √50 to two decimal places.
• Solve: x√25 = 75. Find x.
• Between which two integers does √70 lie?
• What is the square root of 64?
• If x = 3 × √16, find x.
• Find the value of: √1 + √9 + √25.
• Estimate √90 without a calculator.
• True or False: The square root of every number between 1 and 100 is a whole number.

Common Mistakes to Avoid

• Confusing squares with square roots (e.g., mistaking 49 for √49).
• Assuming non-perfect squares have rational roots.
• Forgetting that the square root of a non-perfect square is an irrational (decimal) number.
• Mixing up cube roots and square roots.
• Not practicing estimation skills for quick mental calculation.

Real-World Applications

Square roots are used in various areas of daily life and mathematics. For example, they are essential in finding the side of a square if you know its area, figuring out distances using the Pythagoras theorem, calculations in physics, engineering, and statistics (like standard deviation), and even in finance. Quick recall of Square Root 1 to 100 helps in problem-solving during exams and in practical scenarios.

At Vedantu, we help students learn and master foundational concepts like square roots using comprehensive tables, worksheets, and practice quizzes for better exam results.

In this topic, you have learned about Square Root 1 to 100, how to find and estimate these roots, and why they matter in maths and daily life. Mastering this list builds speed and confidence for both school and competitive exams. Explore more about Squares and Square Roots and use Vedantu’s resources to reinforce your learning.