To estimate a non-perfect square root to the hundredths place without a calculator, you can use the method of approximation. Start by finding the two perfect square numbers that the non-perfect square falls between. Then, determine where your number lies between those two perfect squares. Take the square root of the lower perfect square and the square root of the higher perfect square. Finally, use linear interpolation to estimate the value of the non-perfect square root to the hundredths place.