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 = (2

2) Write 11664 as 116.64 x 10

√10

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 = (2

^{2})^{2 }x (3^{3})^{2}Then, √11664 = 2^{2 }x 3^{3 }= 4 x 27 = 1082) Write 11664 as 116.64 x 10

^{2.}√10

^{2 }= 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