Estimate the square root of 72 to the nearest tenth without using a calculator.

8^2 = 64       9^2 = 81        72 is in between

 

8.something is the answer probably around 8.4   

  try to multiply 8.4  x  8.4  (without a calculator)   then try 8.5 x 8.5 to see which is closest

 

 

another way:

 

sqrt72 = (sqrt 2 x 36) = 6 x sqrt2     I know sqrt 2 is approx  1.414     6 x 1.414   = ~ 8.5  (without a calculator)