Final answer:
To approximate √12, find two perfect squares it lies between, such as 9 and 16. Determine which perfect square it is closer to, then use linear interpolation to find a more accurate approximation. √12 is approximately 3.464.
Step-by-step explanation:
To approximate √12, we can start by finding two perfect squares that it lies between. The two perfect squares that are closest to 12 are 9 (32) and 16 (42). Since 12 is closer to 9, we can approximate √12 to be closer to 3 than to 4. Next, we can use the concept of linear interpolation to find a more accurate approximation. Linear interpolation involves finding the ratio of the difference between 12 and 9 to the difference between 16 and 9, and then multiplying that ratio by the difference between 3 and 4. By doing this calculation, we find that √12 is approximately 3.464.
Learn more about Approximating square roots