Which of the following values is the approximation for the square root of 17?

To determine the square root of 17, it's helpful to start by identifying perfect squares close to 17. The perfect squares immediately surrounding 17 are 16 (which is 4 squared) and 25 (which is 5 squared). Since 17 is between 16 and 25, we know that the square root of 17 must be between 4 and 5.

Specifically, since 17 is just slightly greater than 16, we can infer that the square root will be a bit more than 4. The squares of the options available give us clues:

• Squaring 4.1 results in 16.81, which is less than 17.

• Squaring 4.2 results in 17.64, which is greater than 17.

• The next step is to see where 4.12 falls: squaring it gives us approximately 16.9744, which is still less than 17 but closer than 4.1.

Therefore, 4.12 is a more precise approximation of the square root of 17 than the other values provided. The estimation also becomes clearer through the process of exclusion, as both 4.00 and 4.10