We are tasked with finding two consecutive whole numbers that $\sqrt{127}$ lies between. Here's how to approach it:

1. Find the square root of 127: $\sqrt{127} \approx 11.29$

2. Identify the two whole numbers between which 11.29 lies. The whole numbers are 11 and 12.

Thus, $\sqrt{127}$ lies between the whole numbers 11 and 12.

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Would you like a deeper explanation, or have any questions about the process? Here are 5 related questions to think about:

1. What are the two consecutive whole numbers that $\sqrt{150}$ lies between?
2. Can you find the square root of a perfect square like 144 without approximation?
3. How would you estimate $\sqrt{200}$ without a calculator?
4. What is the square root of a number like 169?
5. How can the concept of square roots be applied in geometry?

Tip: If you know perfect squares close to your number, estimating square roots becomes much easier!