Trick To Find Out Square root quickly

Hey People

 In last topic i covered how to find squares quickly  but what if we have to reverse situations that is we are given the squares and we need to find its root.
For this i will  show  you one trick.

P.S : The trick is applicable to perfect squares only.


To know if given number is perfect square or not click here.


consider any  number say

216

    (256)1/2

method:

check last digit of number and match it with last digit of square from 1 to 10
  here last digit is 6 so 6 comes in  square of 4 and 6.so last digit of square root of 216 will be either 4 or 6
      
                6/4  
           
next take digits except last two digit and take find out largest perfect square available less than the number formed from digits selected
    here 2 is number and 1 is largest perfect square smaller than 2 so square root of 1 is 1

first digit is final i.e. 1

                         
                       1   6 /4 -------->16  or 14

now to decide  from 6 and 4 we will take number between 14 and 16

so 15 square is 225(to find of square of multiple of 5  quickly )

so  256 is greater than 225 so take 16

                      square root of 256 is 16

Question 1:

find square root of following

(7056)1/2
  • 81
  • 83
  • 84
  • 86
  • none of these




Answer

Answer

From last digit 6 we find out last digit of square root is either 4 or 6
now leaving last two digit number formed is 70
square root of largest perfect square number smaller than 70
64 is largest perfect square less than 70 and square root of 64 is 8.
so there are two square root possible for 7056 i.e 84 and 86, to finalize answer find out square root of middle term 85 ( 84<85 br=""> (85)2=7225
7225>7056 so answer is 84
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