Question

To find 5, Beau found 22 = 4 and 32 = 9. He said that since 5 is between 4 and 9, 5 is between 2 and 3. Beau thinks a good estimate for 5 is 2 + 3 2 = 2.5. Is his estimate high or low? How do you know?

Answer 1

Complete question

To find
`√(5)` , Beau found
`2^2 = 4` and
`3^2 = 9` . He said that since 5 is between 4 and 9,
`√(5)`, is between 2 and 3. Beau thinks a good estimate for
`√(5)` , is
`(2 + 3)/(2) = 2.5` Is his estimate high or low? How do you know?

Answer:

The estimation is high because 5 is very close to 4 so
`√(5)` will also be very close to
`√(4)` which is lower than the estimate

In order to get a good estimate

The first step is to choose a number between 2 and 3 let say 2.8 , 2,85 , 2.9 and the square them

i.e

`2.1^2 = 4.41`

`2.2^2 =  4.84`

`2.3^2 =  5.29`

From here we can see that
`√(5)` lies between 2.2 and 2.3 but is closer to 2.2

So a good estimate for
`√(5)` is 2.2

Explanation: