To find the square root of a perfect square number:
- We find the first figure by looking at the first figures and we find two possible last figures by looking at the last figure.
- We find the first figure by looking at the first figures.
- we find two possible last figures by looking at the last figure.
- We then decide which is correct either by considering the digit sums or by considering the square of their mean.
Consider for example:
1.) Square root of 12544
a. We divide the given number into two groups as 125 & 44.
b. Now we will find the nearest square number to the first group (i.e 125)
We have 11 & 12
11^2 = 121 & 12^2 = 144
Now, we need to choose between these two.
Choose the smallest value (i.e below 125) = 121
The square root of 121 = 11. This forms the first part of our answer.
c. As the second group ends with 44, therefore the square root of number ends with either 2 or 8 ( Since 2^2 = 4 & 8^2 = 64).
Here also, we have two answers. We need to find the correct answer.
We will use the digital sum concept, then digital sum of 112^2 = (1+1+2)^2
= 4^2 = 16 = 7. Similarly, 118^2 = (1+1+8)^2 = 1^2 =1.
12544 = ( 1+2+5+4+4) = 16=7
By observing the above two digital sum with that of given number whose square root is to be found.
Therefore, square root of 12544 = 112
2. Square root of 5929
a. Grouping will be 59 & 29.
b. Nearest square number to the first group (i.e 59)
We have 7 & 8
We will choose the first one, (i.e 7) since 7^2 = 49 is less than 59.
c. 2nd group (i.e 29), we will have two choices- 3 & 7
Now the answers are 73 &77
We need to choose one answer between above answers.
DS( 5929) = 5+9+2+9 = 7
DS(73)^2 = 1^2 =1
DS(77)^2 = 14^2 =5^2 =7
Now, comparing the above digital sum(DS). We will come know that 77 is the correct answer.
Therefore, square root of 5929 = 77
Exercise:
Find the square root of
a.) 17161
b.) 4761
c.) 53361
d.) 4356
e.) 9216
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