Vedic maths: Square

Example : Find square of 12

Step 1

1010 is the nearest power of 1010 which can be taken as our base.

The deviation to our base =12−10=2=12−10=2 (To find the deviation, just remove the leftmost digit “11” and you will get it quickly).

Left side of the answer is the sum of the number and deviation. Hence, left side of the answer = 12 + 2 = 14

Step 2

Our base 1010 has a single zero. Therefore, right side of the answer has a single digit and that can be obtained by taking the square of the deviation.

Hence, right side of the answer =22=4=22=4

Therefore, answer =144

Vedic maths: Square roots

Square root of any number means to get a number which is multiplied by itself gives the given number. In the conventional method of finding the square root, the divisor goes on becoming larger at each step. This increases the calculation time as well as the complexity of the problem. Here, we shall try to learn some speedy Vedic Methods of finding the square roots of perfect square numbers. Before proceeding for finding square roots, let us have a look into the known facts of squares and square roots.

The basic rules for extracting square roots are :

- The given number is arranged in two-digit groups from right to left; and a single digit (if any) left over at the left and is counted as a group by itself.
- The number of digits in the square root will be the same as the number of twodigit groups in the given number including a single digit group (if any). Thus, 36 will count as one group, 169 as two groups and 1225 as two groups.
- If the number contains n digits then the square root will contain n / 2 (when n is even) and n + 1 / 2 (when n is odd) digits. Thus, one or two digit number will have the square root of one digit, three and four digit number will have the square root of two digits, 5 and 6 digit number will have the square root of 3 digits and so on.

1² = 1, 2²=4 , 3²=9 , 4²=16 , 5²=25, 6²=36, 7²=49, 8²=64 , 9²=81

This means :

- unit digit of the perfect square number is 1, 4, 5, 6, 9 or 0.
- a perfect square number cannot end in 2, 3, 7 or 8.
- the relation between the unit digit of a perfect square number and the unit digit of its square root is as follows :

Unit digit of the number 1 4 5 6 9 0

Unit digit of square root 1 or 9 2 or 8 5 4 or 6 3 or 7 0

- If there are odd number of zeros at the end (on right side) of a number, then it will not be a perfect square.

Cube roots in vedic maths

Find Cube Root of 4913

Step 1

Identify the last three digits and make groups of three three digits from right side. i.e., 49134913 can be written as

4, 913

Step 2

Take the last group which is 913.913. The last digit of 913913 is 3.3.

Remember point 2, If last digit of perfect cube=3,=3, last digit of cube root =7=7

Hence the right most digit of the cube root =7

Step 3

Take the next group which is 44

Find out which maximum cube we can subtract from 44 such that the result ≥0≥0

We can subtract 1 3 = 1 from 4 because 4 − 1 = 3 (If we subtract 2 3 = 8 from 4 , 4 – 8 = − 4 which is < 0 )

Hence the left neighbor digit of the answer = 1 i.e., answer = 17

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