Final answer:
To better estimate √2, use a number line between 1 and 2, knowing √2 will be between these numbers. Remark that √2 is closer to 1.4, as it's a good approximation, and label this point on the number line.
Step-by-step explanation:
To find a better estimate of √2, you can start by knowing that √1 = 1 and √4 = 2. Since 2 is between 1 and 4, √2 must be between 1 and 2. A good approach is to use a number line to help visualize where √2 might fall.
First, draw a number line with 1 and 2 as your reference points. Knowing that √2 is roughly 1.4 (since 1.42=1.96), you can estimate that √2 is closer to 1.4 than to 1.5 because 1.52 is 2.25, which is greater than 2. Place a mark slightly to the left of the midpoint between 1.4 and 1.5 on your number line to represent √2.
Label your estimate on the number line accordingly. Remember, the exact value of √2 is irrational and cannot be precisely represented on the number line, but 1.4 is a useful approximation for most purposes.