Hello!
To decide whether or not a number is rational, it has to be able to be written as a fraction. For example, 0.333333 is rational because it can be written as 1/3 because you can use the formula to turn repeating numbers into a fraction. Numbers like pi are not rational because they have no repeating pattern and go on forever. They cannot be written as a fraction, and therefore are not rational.
To find the square roots of these numbers, we can find it out of the denominator.
For 1/9 we know that the square root of 9 is 3. Where our original numerator was 1, we do not have to divide it at all to match the root, so it stays as 1/3, which is the square root of 1/9. It is a rational number, so the 2nd and 3rd options in the problem cannot be the answer.
Now we have to find the square root of 49/25. Notice that both the numerator and denominator have perfect squares. We can just find the squares and make it a fraction. This is 7/5, but is it a rational number? 7/5=1.4, which can be written as a fraction and is a rational number.
We have come to the conclusion that both of these squares are rational. This means our answer is the last one.
I hope this helps!
