Answer:
The radical approximations of 7.07, 7.21, and 7.93 to the nearest whole number are:
2.65
2.68
2.82
Explanation:
Sure, here's a step-by-step explanation of finding the approximate square root of 7.07, 7.21, and 7.93 to the nearest whole number:
Start by finding an approximate square root by making an educated guess or by using a calculator.
Use the initial guess to determine if the number is closer to the actual square root or to a smaller or larger value.
Refine the estimate by averaging the guess and the number divided by the guess.
Repeat the process of refining the estimate until a satisfactory level of accuracy is reached.
Here's an example for 7.07:
An educated guess for the square root of 7.07 could be 2.7
Dividing 7.07 by 2.7 gives an estimated value of 2.61, which is closer to the actual value.
To get a more accurate estimate, the average of 2.7 and 2.61 (2.655) is taken as the new estimate.
Repeat steps 2 and 3 until the desired level of accuracy is achieved.
After several iterations, the square root of 7.07 is approximately equal to 2.65.
Similarly, you can find the approximate square roots of 7.21 and 7.93.