Given that:
Consider it is [tex]\sqrt{10}[/tex] instead of 10 on two places.
[tex]\sqrt{10}[/tex] is between 3 and 4. So, Beau thinks a good estimate for [tex]\sqrt{10}[/tex] is = 3.5.
Solution:
To find [tex]\sqrt{10}[/tex], Beau found 3² = 9 and 4² = 16.
He said that since 10 is between 9 and 16.
Since 10 is close to 9, therefore [tex]\sqrt{10}[/tex] must be close to 3. So, Beau's estimate is high.
Now,
[tex](3.1)^2=9.61[/tex]
[tex](3.2)^2=10.24[/tex]
Since, 10 lies between 9.61 and 10.24, therefore [tex]\sqrt{10}[/tex] must be lies between 3.1 and 3.2.
[tex]\dfrac{3.1+3.2}{2}=3.15[/tex]
Therefore, the estimated value of [tex]\sqrt{10}[/tex] is 3.15.
