How to find the square root of 11,664?

4

4 Answers

Noor-ul-Elmah Hasan Profile
Using prime factorization




 

 



  2
  11664


  2
  5832


  2
  2916


  2
  1458


  3
  729


  3
  243


  3
  81


  3
  27


  3
  9


  3
  3


 

  1

( 2 x 2 ) ( 2 x 2) ( 3 x 3 ) ( 3 x 3 ) ( 3 x 3)
( 2 x 2 x 3 x 3 x 3)^2
108 ( the square will  get cut in under root as its power is 1/2 )
108 is the square root  of 11664

( please tell , is it helpful or nor )
Vin Ginge Profile
Vin Ginge answered
Assuming that you can't use a calculator etc. And that the answer is an integer.

1) Express 11664 in terms of its prime factors.
11664 = 2^4 x 3^6 = (22)2 x (33)2 Then, √11664 = 22 x 33 = 4 x 27 = 108

2) Write 11664 as 116.64 x 102.
√102 = 10, and by observation, the square root of 116.64 lies be 10 and 11.
As the final digit of 116.64 is 4 then the number being squared is either 10.2 or 10.8...the latter being the correct result and thus the complete square root = 10 x 10.8 = 108.
thanked the writer.
Iris Hinds
Iris Hinds commented
Thank you very much Vin Ginge. You were very helpful.
Oddman
Oddman commented
(100+x)^2 = 10,000 + 200x +x^2, so the four low-order digits are a clue. 1600=200*8, and 64=8^2.
Mark Mottian
Mark Mottian commented
I that was a real smart method that you used in your first point!

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