How to find the square root of 11,664?
108
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.
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.
Use a calculator