Question

Find a close estimate for square root of 45. (without a calculator) Round your answer two decimal places

Answer 1

Factor45 under the radical sign √45= √9×5= √3²×5
Simplify Powers 
3√5 =Answer approx = 6.70

Answer 2

You know that 7*7 is 49, and 6*6 is 36. Now you know it will be 6._. 6*7 is 42, so think of that as 6.5^2. You know that it will most likely be less than 6.8 since it is so close to being 7*7, which is 4 above your desired number. This leaves 6.6 to 6.8 as your estimate. Personally, I would go straight in the middle and choose 6.7. 

I hope this helps!