Question

What 2 integers does the square root of 3 lie between?

Answer 1

1 and 2

Explanation:

The sqrt of 2 is equal to approximately 1.4. The sqrt of 4 is equal to 2. As we know the sqrt of 3 lies somewhere between these two sqrts, we know that i must also lie between the integers 1 and 2.

Answer 2

The square root of 3 lies between 1 and 2.

Explanation:

Squaring something is the inverse of taking the square root, so if we start by squaring some numbers, we want it to come out close to 3. The integers squared that are above and below 3 will be the 2 integers that the square root of 3 lies between.

Anything `3^2` and above isn't going to help- it'll be too big.
(You can try it if you'd like- `3^2=9`, which is a lot more than 3.)
Okay, so try `2^2`. That equals 4, which is pretty close, just a bit larger than 3.
Let's try the very next one down, `1^2`. That equals 1, which is less than 3.
Great! we've just found the 2 integers that the square root of 3 lies between, 1 and 2!

If you're interested, the actual value of `sqrt3=1.732050808...` which is indeed between 1 and 2.