Question

To find 10, Beau found 32 = 9 and 42 = 16. He said that since 10 is between 9 and 16, 10 is between 3

Answer 1

Given that:

Consider it is $\sqrt{10}$ instead of 10 on two places.

$\sqrt{10}$ is between 3  and 4. So, Beau thinks a good estimate for $\sqrt{10}$ is = 3.5.

Solution:

To find $\sqrt{10}$, Beau found 3² = 9 and 4² = 16.

He said that since 10 is between 9 and 16.

Since 10 is close to 9, therefore $\sqrt{10}$ must be close to 3. So, Beau's estimate is high.

Now,

$(3.1)^2=9.61$

$(3.2)^2=10.24$

Since, 10 lies between 9.61 and 10.24, therefore $\sqrt{10}$ must be lies between 3.1 and 3.2.

$\dfrac{3.1+3.2}{2}=3.15$

Therefore, the estimated value of $\sqrt{10}$ is 3.15.