Question

Using the ratio of perfect squares method, what is the square root of 22 rounded to the nearest hundredth?

Answer 1

The ratio of perfect squares method can tell you that sqrt(22) is between 4 and 5, because 4^2=16<22<25=5^2

Estimating using Newton's method will give you an estimate good to the hundredth and more, as follows.
Find the closest integer estimate. 4^2=16=22-6, 5^2=25=22+3, so 5 is closer (but too big).
We find the estimate by calculating
5-(5^2-22)/(2*5)=4.70
which is almost good to the hundredth.
To get more accuracy, we use 4.7 as the estimate:
4.7-(4.7^2-22)/(2*4.7)=4.6904

Answer 2

thank you! @mathmate

Answer 3

You're welcome! :)