Question

What is the sum of all the integers between the square root of 10 and the square root of 47

Answer 1

What's the square root of  10 ?
     3²=9  and  4²=16
     So  √10  is somewhere between  3  and  4 .

What's the square root of  47 ?
     6²=36  and  7²=49
     So  √47  is somewhere between 6 and 7 .

The integers between √10 and √47 are  4,  5, and  6 .

Their sum is (4 + 5 + 6) = 15 .

Answer 2

First estimate the square root of 10, about 3.16
and then the square root of 47, about 6.85
now what are the integers in between 3.16 and 6.85:
4,5,6
now add them all 
4+5+6
=15
Hope this helps.