Square Roots & Cube Roots

The square root of a number 'k' is a number denoted by a number such that the number i.e., when multiplied by itself is equal to the given number i.e. k
e.g., = 13, since 13 × 13 = 169
= 41, since 41 × 41 = 1681

Square Roots by Factors:

Steps:
(1) Find out prime factors of the given number.
(2) Arrange the factors in pairs.
(3) Take one factor from each pair.
(4) Find the product of these factors, which represents the square root of the given number:

Square of a number ending in 5:
Multiply the ten's digit 'n' by the next higher integer (n + 1) and write 25 to the right of the product.


Square of a number ending in 25:
Multiply the hundred's digit by a number consisting of the hundred's digit with a 5 to its right and annex 625 to the right of the product.

Example Find the square root of 1936

To find the prime factors of 1936 we shall use successive divisions method.

100 (Or we could divide 193600 by 100, 4 , 4 and 121 (the last perfect square factor). The idea is to have divisions by 4 , 9 , 16 , 25 , 100 or any other visible perfect square - as it will save a lot of time)

Square Root of decimal numbered
Steps: (a) Pairing after decimal is a must. (b) If there are odd number of digits after decimal add zero to make full pairs. (c) Find square root of the number without consideration of decimals and put decimals before as many as digits as many pairs are.