Question

What is the sum of the integers between the square root of 12 and 40?

Answer 1

1.

the closest perfect squares of 12 are 9 and 16, 

that is 9<12<16

so 
$\sqrt{9}\ \textless \ \sqrt{12}\ \textless \ \sqrt{16}$

$3\ \textless \ \sqrt{12}\ \textless 4$

this means, $\sqrt{12}$ is  3 point something...


2.

similarly 

36<40<49

so

$\sqrt{36}\ \textless \ \sqrt{40}\ \textless \ \sqrt{49}$

$6\ \textless \ \sqrt{40}\ \textless \ 7$

which means $\sqrt{40}$ is 6 point something...

3. 

the sum of the integers between the square root of 12 and 40 is the sum of 4, 5 and 6, since 4 is the smallest integer after root 12, and 6 the greatest integer to before root of 40.


Answer: 15