Question

How many integers fall between the square root of 7 and the square root of 77 on a number line

Answer 1

$\sqrt7$ is between 2 and 3. $\sqrt{77}$ is between 8 and 9. So, all the integers between $\sqrt7$ and $\sqrt{77}$ are the integers from 3 to 8, inclusive. This is a total of $\boxed6$ integers.

Answer 2

There are 6 integers between sqrt7 and sqrt77.

Explanation:

Sqrt9, sqrt16, sqrt25, sqrt36, sqrt49, sqrt64 are all between sqrt7 and sqrt77. Since these are all perfect squares, they simplify to integers.

sqrt9 = 3

sqrt16 = 4

sqrt25 = 5

sqrt36 = 6

sqrt49 = 7

sqrt 64 = 8

There are 6 integers between sqrt7 and sqrt77.