Complete question
To find [tex]\sqrt{5}[/tex] , Beau found [tex]2^2 = 4[/tex] and [tex]3^2 = 9[/tex] . He said that since 5 is between 4 and 9, [tex]\sqrt{5}[/tex], is between 2 and 3. Beau thinks a good estimate for [tex]\sqrt{5}[/tex] , is [tex]\frac{2 + 3}{2} = 2.5[/tex] Is his estimate high or low? How do you know?
Answer:
The estimation is high because 5 is very close to 4 so [tex]\sqrt{5}[/tex] will also be very close to [tex]\sqrt{4}[/tex] 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
[tex]2.1^2 = 4.41[/tex]
[tex]2.2^2 = 4.84[/tex]
[tex]2.3^2 = 5.29[/tex]
From here we can see that [tex]\sqrt{5}[/tex] lies between 2.2 and 2.3 but is closer to 2.2
So a good estimate for [tex]\sqrt{5}[/tex] is 2.2
Step-by-step explanation:
