Question

What is the sum of all the integers between the square root of 19 and the square root of 77?

Answer 1

Since we are only dealing with integers, we do not need to worry about decimals. Therefore, finding the exact values of sqrt(19) and sqrt(77) is not important. We can just estimate.

19 is between 16 and 25 (which are 4^2 and 5^2), so the square root of 18 is some number between 4 and 5.

77 is between 64 and 81 (which are 8^2 and 9^2), so the square root of 77 is some number between 8 and 9.

So the integers (whole numbers) that are between our two sqaure roots are 5, 6, 7, and 8.

Add them up and we have our answer.

5+6+7+8 = 26