Final answer:
The square root of 3 is approximately 1.732, and the square root of 2 is approximately 1.414. For arithmetic operations and handling exponentials, precision in terms of decimal places and significant figures is vital, and for higher roots like square roots, a calculator is a useful tool.
Step-by-step explanation:
The square root of 3 as a decimal is approximately 1.732, and the square root of 2 is approximately 1.414. These values can be found using a calculator as most calculators have a square root function. To further explain the process, when taking the square roots of exponentials, if you have a number like 3¹.⁷ (which is 3 to the power of 1.7), you may simplify the process by taking the tenth-root of 3 and raising it to the 17th power. This is an example of expressing a number using fractional powers.
In general, when you are performing operations like addition, subtraction, multiplication, and division, you need to be mindful of the significant figures and decimal places. For addition and subtraction, the result should have the same number of decimal places as the number with the smallest number of decimal places in the original numbers. For multiplication and division, the result should have the same number of significant figures as the number with the least significant figures.
When dealing with square roots or higher roots in mathematical problems, including equilibrium problems, it is essential to know how to carry out these operations on a calculator. Commodious understanding and flexibility with numbers are encouraged, though exactness is not always requisite. It is usually better to work with a reasonable number of decimals that reflect the precision of the data at hand.