Quickest Way to find Square Root of two Numbers | Vedic Maths tricks for fast calculation

Vedic Maths techniques are the best techniques that performs our calculations with rapid speed. Vedic Mathematics is a collection of Techniques/Sutras to solve mathematical arithmetics in easy and faster way. It consists of 16 Sutras (Formulae) and 13 sub-sutras (Sub Formulae) which can be used for problems involved in arithmetic, algebra, geometry, calculus, conics.
Vedic Mathematics is a system of mathematics which was discovered by Indian mathematician Jagadguru Shri Bharathi Krishna Tirthaji in the period between A.D. 1911 and 1918 and published his findings in a Vedic Mathematics Book by Tirthaji Maharaj
Veda is a Sanskrit word which means ‘Knowledge’.
Using regular mathematical steps, solving problems sometimes are complex and time consuming.

The square root of a number is the inverse operation of square of number.
Example
Number Square of the number Square root of the number
6^2 6 × 6 = 36 √36=6
8^2 8 × 8 = 64 √64=8
12^2 12 × 12 = 144 √144=12

Points to be remembered before finding the square root of any number :

1. The given number is arranged as a group of two numbers from right to left. If a single number has remained at the left, then it is also considered as one group.
2. The number of groups derived for the given number will be the number of digits of the square root of that number.

Example : √25=5
, here there are two digits so one group. So, the square root of 25 is 5.
√169=13, the number forms two groups (1, 69), so the square root is two-digit number 13.
3. If the square of a number is an odd number, then the square root is also an odd number, and if the square is an even number, then the square root is also an even number.

Logic to find the square root

Observing the square of numbers from 1 to 9, we can analyze that an exact square ends with 1,4,5, 6,9, and 0 square root. These numbers will be rational numbers.

If the square of the number ends with 2,3,7 and 8 then its square root will be an irrational number.

Square root of perfect square number:
Number:√3969
Step
39 | 69 Grouping: from right to left
38 is greater than 36, the perfect square number of 62, and 69 is lesser than 64, which is a perfect square number of 82
3600 | 6400
602 | 802 Therefore the given number lies between 3600 and 6400 that means there square number will be between 60 and 80
So the first number in the square root will be 6
The number in the units places is 9 so the square number should be ending with 3 or 7 (as discussed above)
The square root of the given number should be either 63 or 67
Applying digit sum method to find the square root
63 = 3969
(6 + 3) = 3+9+6+9
9 = 2 + 7
9 = 9 So the square root of number 3969 is 63
Answer : 3969 = 63

Square root of imperfect square number :
Number Steps
√2
The given number is not a perfect square
1 + 1 = 2. or
4 - 2 = 2 The nearest square number is 1 and 4
1 + 1/2
1 + 0.5
1.5 Square root of 1 is 1, add (1 ÷ [ 1 + 1]) i.e 1 divide by twice the perfect square number
1.5 The same when calculated in calculator gives 1.414 which is approximately equal to 1.5
√20
√2
25 - 5 = 20 25 is the perfect square of 5 subtract it from (1/10) 1 divide by twice the perfect square
25 - 5/10
5 - 0.5
4.5

The same when calculated in calculator gives 4.47 which is approximately equal to 4.5

After learning a few of the tricks to find square and square roots of the number, one will be able to easily find the square numbers and their square roots without any help from calculators. These tricks are very helpful in solving aptitude problems related to square and square roots in competitive exams.

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Voice Over: Dheemraj
Music: Maestro Tlakaelel
Artist: Jesse Gallagher

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