What two integers does square root 7 fall between

Answer 1

When it is asking "what two integers does √7 fall between", it is asking where on the number line with the value of √7 (7 being a non-perfect square and therefore having an infinitely long decimal expansion) be placed. Let's take a look at a number line and perfect squares:

First, perfect squares are numbers in which their square root is equal to a whole number. For example √4=2, Therefore, 4 is a perfect square.

For this question, we want to think in reverse: Which integer numbers, when squared fall directly below and above 7.

0----1----2----3----4----5----6----7----8----9----10

0²= 0

1²=1

2² = 4

3³ = 9

4² = 16

....

As we can see, seven falls between 2 squared, which is 4, and 3 squared, which is 9. Reversing this, the square root of 4 is 2 and the square root of 9 is 3. Therefore, the value of the square root of 7 will be between the square root of 4 and the square root of 9, which are the integers 2 and 3.