Which of the following approximates the square root of 2.83?

To determine which value approximates the square root of 2.83, we can analyze the square roots of numbers close to 2.83:

The square root of 2.83 is between the square roots of 2.25 (which is 1.5) and 3.24 (which is approximately 1.8) since those squared give values just below and just above 2.83. This can help us establish boundaries.

Calculating further, the square root of 2.5 is approximately 1.58, and the square root of 3 is roughly 1.73. Therefore, we can conclude that since the value of 2.83 is less than 3 and greater than 2.5, its square root is between 1.58 and 1.73—thus it’s closer to 1.7 than it is to 1.6.

Now, when we look at the choices provided, the best representation of what the square root of 2.83 is would be related to the original number itself, rather than the numbers directly given. Among the options presented, one comes closest as it is identical to the value being squared; hence, choosing the corresponding choice