This is a clear and efficient method based on Vedic Math principles, and it works perfectly for numbers that are perfect squares! You can easily use this technique to find square roots for any perfect square.
Before Finding the Square Root, It's Important to Memorize the Squares of the Following Numbers.
Number | Square |
---|---|
1 | 1 |
2 | 4 |
3 | 9 |
4 | 16 |
5 | 25 |
6 | 36 |
7 | 49 |
8 | 64 |
9 | 81 |
10 | 100 |
Note: A perfect square number can never end with the digits 2, 3, 7, or 8.
Step 1: The given number ends with 6. Therefore, the square root must end with either 4 or 6.
(Refer to a squares table: 4² = 16, 6² = 36).
Step 2: Next, remove the digit to the left of the last digit of the number.
Step 3: Find the approximate square root of the remaining number (2).
For example, (1 x 1 = 1), which is less than or equal to 2.
Step 4: Consider the two options: (14)² or (16)². One of these will be the square root of 256.
We already know the square of numbers that end with 5.
Therefore, for (15)² = 1 × (1 + 1) / 5² = 2 / 25 = 225
Step 5: (15)² = 225, which is less than 256. Therefore, the root cannot be 14.
Conclusion: The square root of √256 is 16.
Step 1: The given number ends with 9. Therefore, the square root must end with either 3 or 7.
(Refer to a squares table: 3² = 9, 7² = 49).
Step 2: Next, remove the digit to the left of the last digit of the number.
Step 3: Find the approximate square root of the remaining number (10).
For example, (3 x 3 = 9), which is less than or equal to 10.
Step 4: Consider the two options: (33)² or (37)². One of these will be the square root of 1089.
We already know the square of numbers that end with 5.
Therefore, for (35)² = 3 × (3 + 1) / 5² = 12 / 25 = 1225
Step 5: (35)² = 1225, which is larger than 1089. Therefore, the root cannot be 37.
Conclusion: The square root of √1089 is 33.
Step 1: The given number ends with 1. Therefore, the square root must end with either 1 or 9.
(Refer to a squares table: 1² = 1, 9² = 81).
Step 2: Next, remove the digit to the left of the last digit of the number.
Step 3: Find the approximate square root of the remaining number (65).
For example, (8 x 8 = 64), which is less than or equal to 65.
Step 4: Consider the two options: (81)² or (89)². One of these will be the square root of 6561.
We already know the square of numbers that end with 5.
Therefore, for (85)² = 8 × (8 + 1) / 5² = 72 / 25 = 7225
Step 5: (85)² = 7225, which is greater than 6561. Therefore, the root cannot be 89.
Conclusion: The square root of √6561 is 81.
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