## Vedic Math Square Roots

## Square Roots of Perfect Squares

To find out the square root of exact squares first of all we should know if the number is a perfect square or not. To find out if any given number is as exact square we should follow the following fundamental rules

- A perfect square if it ends in 0, 1, 4, 5, 6 & 9

- A number is not a perfect square if it ends in 2, 3, 7, & 8

- A number should end in even numbers of zeros

- If the number ends in '6', than the second last digit should be odd.

- If the number does not end in '6', than its second last digit should be even.

- If the number is even its last two digits should be divisible by '4'.

- If the given number has 'n' digits then its square root will have, n/2 digits if 'n' is even, or (n + 1)/2 digits if 'n' is odd.

#### The basic or fundamental rules governing the extraction of the square root, are as follow.

- The given number is first arranged in two-digit groups (from right to left) ; and a single digit (if any) left over (at the left-hand-end) is counted as a simple group by itself.

- The number of digits in the square root will be the same as the number of digit-groups in the given number itself (including single digit if any such there be).

- So, if the square root contains 'n' digits, the square must consist of 2n or 2n-1 digits.

- And, conversely, if the given number has 'n' digits, the square root will contain n/2 or n+1/2 digits.

- But, in case of pure decimals, the number of digits in the square is always double that in the square root.

- The square of first nine natural numbers are 1, 4, 9, 16, 25, 36, 49, 64 and 81. This means that an exact square cannot end in 2, 3, 7 or 8

#### What is square root?

To understand square root it will be important to understand what are squares. Squaring of a number can be defined as multiplying a number by itself. Thus, when we multiply 4 by 4 we are said to have 'Squared' the number four. Thus we can say that '16' is the square of '4' and '4' is the "Square Root" of '16'

#### The vedic math sutra we will be using is "Vilokanam" that is "By mere observation"

In this method we formulate tables of square of numbers and their square roots. Following the sutra by mere observing the tables, we can find out the **'last**** digit'** of our square root and we find out the** 'first digit'** of the square root by observing the first group of the number