Question

square root of 2.89 how to work this out

Answer 1

well you know the square root of 2 is approximately 1.414 and the square root of 4 is 2. (you might have memorized the square root of 3, but you probably haven't.) so the square root of 2.89 is somewhere between 1.414 and 2.
if you know your squares, you know that 17^2 is 289. thus, 1.7^2 is 2.89. this agrees with our approximation of between 1.414 and 2.