### Instruction: Between what two consecutive integers on the number line is the graph of the sum $\sqrt{30} + \sqrt{50}$ located? Enter your answer in the form "$m$ and $n$", where $m$ and $n$ are replaced by appropriate numbers.### Response: I know that $\sqrt{30}$ and $\sqrt{50}$ are both irrational numbers, meaning they cannot be written as fractions of integers. So their sum will also be irrational.
However, I can use some estimates to find an approximate value for their sum.
For example, I know that $\sqrt{25} = 5$ and $\sqrt{36} = 6$, so $\sqrt{30}$ must be between 5 and 6, closer to 5.
Similarly, I know that $\sqrt{49} = 7$ and $\sqrt{64} = 8$, so $\sqrt{50}$ must be between 7 and 8, closer to 7.
So, using these estimates, I can say that $\sqrt{30} + \sqrt{50}$ is between 12 and 14, closer to 12.
To be more precise, I can use a calculator to find that $\sqrt{30} \approx 5.48$ and $\sqrt{50} \approx 7.07$.
Adding these values, I get $\sqrt{30} + \sqrt{50} \approx 12.55$.