How does the square of that approximation compared to 31?

Question

Approximate square root 31 with a decimal to the nearest hundredth. How does the square of that approximation compared to 31?

Answer 1

31 is between the square numbers 25 and 36, whose respective square-roots are 5 and 6.  Lets take the median of 25 and 36 to see how far in the middle 31 is.

 

(25 + 36) / 2 = 61 / 2 = 30.5

 

This is close to 31.

 

 

Take the median of the square-roots.

 

(5 + 6) / 2 = 11 / 2 = 5.5   This is the median square-root.

 

 

Square-root of 31 is between 5.5 and 6.

 

√31 = 5.55

Answer 2

5² = 25

6² = 36

 

31 is just over halfway between

5² and 6² .... A reasonable 

approximation of √31 may be about

5.55

 

5.55² = 30.8025