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 $\sqrt{5}$ , Beau found $2^2 = 4$ and $3^2 = 9$ . He said that since 5 is between 4 and 9, $\sqrt{5}$, is between 2 and 3. Beau thinks a good estimate for $\sqrt{5}$ , is $\frac{2 + 3}{2} = 2.5$ Is his estimate high or low? How do you know?

Answer:

The estimation is high because 5 is very close to 4 so $\sqrt{5}$ will also be very close to $\sqrt{4}$ 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 $\sqrt{5}$  lies between 2.2 and 2.3 but is closer to  2.2

So a good estimate for $\sqrt{5}$ is 2.2

Step-by-step explanation: