Question

What numbers does the square root of 125 fall between?

9 and 10
11 and 12
13 and 14
15 and 16

Answer 1

The answers are "11 and 12"

Explanation:

In order to determine the square root of 125, we have to estimate the nearest square root. We elevate some numbers near of 125. It is useful to know some approximation:

`10^2=100\\11^2=121\\12^2=144\\13^2=169`

Then, the value "125" is in between
`11^2 and 12^2`.

`11^2<125<12^2\\√(11^2)<√(125)<√(12^2)\\ 11<√(125)<12`

Finally the answers are "11 and 12"