Square Roots
Find roots of perfect squares instantly.
Core Concepts
To find the square root of a perfect square, we observe the last digit and the magnitude.
Step 1: Last Digit
Look at the last digit of the number:
• Ends in 1 → Root ends in 1 or 9.
• Ends in 4 → Root ends in 2 or 8.
• Ends in 5 → Root ends in 5.
• Ends in 6 → Root ends in 4 or 6.
• Ends in 9 → Root ends in 3 or 7.
Step 2: First Part
1. Strike out the last 2 digits.
2. Find the nearest square BELOW the remaining number.
3. This gives the first digit.
Solved Examples
Example 1: √1764
Question: Find the square root.
• Ends in 4 → Last digit is 2 or 8.
• Strike 64. Remaining is 17.
• Square below 17 is 16 (4²). So first digit is 4.
• Options: 42 or 48.
• Check middle: 45² = 2025.
• 1764 is less than 2025, so choose smaller.
• Answer: 42.
Example 2: √3136
Question: Find the square root.
• Ends in 6 → Last digit is 4 or 6.
• Strike 36. Remaining is 31.
• Square below 31 is 25 (5²). First digit is 5.
• Options: 54 or 56.
• Check: 5 × 6 = 30. 31 > 30, so choose larger.
• Answer: 56.
Example 3: √2025
Question: Find the square root.
• Ends in 5 → Last digit is 5.
• Strike 25. Remaining is 20.
• Square below 20 is 16 (4²).
• Answer: 45.
