Square Roots | Shortcuts to find square root of a number |

Tirthaji Maharaj has classified tricks to find square roots in Vedic Mathematics in Specific and General Methods. Specific Multiplication Methods can be applied to a Perfect Square. While General Square Root Methods can be applied to any type of number.

Facts for Square Roots Math tricks :

Squares of numbers from 1 to 9 are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
Square of a number cannot end with 2, 3, 7, and 8. OR number ending with 2 , 3, 7 and 8 cannot have perfect squareroot.
Squareroot of a number ending with 1 (1, 81) ends with either 1 or 9 (10’s compliment of each other).
Squareroot of a number ending with 4 (4, 64) ends with either 2 or 8 (10’s compliment of each other).
Squareroot of a number ending with 9 (9, 49) ends with either 3 or 7 (10’s compliment of each other).
Squareroot of a number ending with 6 (16, 36) ends with either 4 or 6 (10’s compliment of each other).
If number is of ‘n’ digits then square root will be ‘n/2’ OR ‘(n+1)/2’ digits.

Based on the facts, square root method can be calculated as follows:

Specific Method: This method shows how find square root of a PERFECT square.
General Method: This method shows trick to find square root of any of PERFECT of IMPERFECT Square.

Specific Method:

This shortcut method of Square Roots can be applied whenever number is perfect square.

Example:

Square root of 2209

Number ends with 9, Since it’s a perfect square, square root will end with 3 or 7.
Need to find 2 perfect squares (In Multiplies of 10) between which 2209 exists.
Numbers are 1600(40²) and 2500(50²).
Find to whom 2209 is closer. 2209 is closer to 2500. Therefore squareroot is nearer to 50
Now from Step 2, possibilities are 43 or 47 out of which 47 is closer to 50
Hence squareroot = 47.

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