Firstly, to be able to perform this trick so fast and accurate, you will need to study and know the square of 1 to 9 off hand.
Don't bother your self too much about the squares because they are right here.
12 = 1
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
Now let's get started
If you can study all the following step carefully, trust me you will be calculating the square root of perfect square off hand ✋.
Example 1
Step 1 – pick the last number (the unit) which is 4. Then we look at the table above to check for the squares that end with 4. So here it is.
22 = 4
82 = 64
Sotherefore, Square of 2 and 8 ends with 4 which are 4 and 64 respectively.
Step 2 – Both 2 and 8 will be note down because one of them will later be the last number (The unit) of the of the square root we are looking for.
Step 3 – Now, we ignore the tens digit and move on to to the first number which is the hundreds digit (7)
Note that if we are ask to find square root of four or five digit number we still ignore the tens digit and consider the rest as one number
Now let's check the square closest to 7 ( less than 7).
Hmm it is 4, the square of 2.
And now we've got the tens digit of the square root to be 2 because since 4 is the closest square less than 7 and 2 is the square root of 4
Step 4 – In this step, we multiply the tens digit we just discovered (2) by the next number after it (3)
That's 2 X 3 = 6
Step 5 This step is quite complicated so let's be careful here.
Now we are going to compare 6 (the multiple in step 4) with 7 (The hundreds digit of our square). Also, we recall back to step two where 2 and 8 are been noted down.
After comparing, We all know that 7 is greater than 6 so therefore will we pick 8 which is the bigger number as the unit digit of the square root.
But note if the hundreds digit of the square (7) is lesser than the multiple in step 4, the smaller number (2) will be considered as the unit digit of the square root
So Therefore
Let’s look at 1 more example to understand this trick more better
Example 2 – 2116
Step 1 – 6 – 4 and 6 ( number having 6 as the last number of their square)
Step 2 – 4 and 6 ( 4 and 6 noted down)
Step 3 – 21, 4 (16) (we skip the tens digit then consider the rest (21 as one number) the look for the nearest square less than 21. Which 4 is the square root and also the tens digit of the square root we are looking for)
Step 4 – 4 x 5 = 20 ( 4 is then multiply by the next number after it)
Step 5 – 21 > 20 ( The total in step four is then compared with 21, and since it greater we pick the bigger number in step 2 as the unit digit)
Then final answer is 46.
