Square roots of perfect squares

    Slide1

 

 

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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About Praveenkumar P Kalikeri

ABOUT US Hey,Thanks for dropping by .First I would like to Appreciate for your love towards the Mathematics Subject. My name is Praveenkumar Kalikeri. I'm an Engineering Student from Karnataka , India. My Passion for Mathematics , encouraged me to start this blog . I Started loving the Mathematics subject from my schooling days.I was greatly motivated by teachers, parents who always helped me .        Numbers have Beauty !! They fascinated me .. As we all know best method to try out something new is to study old theories , concepts , its drawbacks, etc. I ,myself Started learning Vedic Mathematics at age of 15. Here , I will share vedic maths tricks learned and modified by me in simple manner which will be useful in various competitive exams. "If You Believe , You Can Do".
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