Final answer:
Estimating the square root of a number involves finding the two whole numbers it falls between, adjusting for exponentials when necessary, and paying attention to addition and subtraction principles. For instance, the square root of 12 falls between 3 and 4, closer to 3 because 12 is closer to 9 (3 squared) than to 16 (4 squared).
Step-by-step explanation:
When estimating square root values, you are trying to find which two whole numbers a square root number falls between. For example, if you need to estimate the square root of a number such as 12, you would look at the closest perfect squares around it, which are 9 (3 squared) and 16 (4 squared). Therefore, the square root of 12 is somewhere between 3 and 4. To refine this estimate, you can observe that 12 is closer to 9 than to 16, so its square root will be closer to 3 than to 4.
To accurately work with exponentials when taking square roots, adjust the power so it is divisible by 2. For the square root of an exponential term like 10´, you would divide the exponent by 2 to get (10´)^(1/2) = 10², which is 100.
When working with addition and subtraction, the basic principle is to combine like terms and pay close attention to the signs of the numbers involved. With whole numbers, you simply add or subtract the absolute values and assign the correct sign to the result.