Final answer:
The square root of 30 to two decimal places is 5.48. This is found by initially estimating that it lies between 5 (the square root of 25) and 6 (the square root of 36), and then using a calculator which gives a more precise value. The final answer must be rounded appropriately to two decimal places.
Step-by-step explanation:
To find the square root of 30 to two decimal places, you would likely use a calculator, as the square root of 30 is not a whole number and is somewhat complex to calculate manually. Still, we can approximate it using estimation and refinement techniques for instructional purposes. First, recognize that the square root of 25 is 5 and the square root of 36 is 6, so the square root of 30 must lie between those two values. You can then use a method such as the Babylonian method or trial and error to get a more precise value.
When using a calculator, you would get a non-rounded value with several decimal places. The key in rounding to the correct number of significant figures or decimal places is knowing that you need to look at the digit after the place to which you are rounding. If this digit is 5 or greater, you round up. If it is less than 5, you keep the last desired digit the same. Following this rule, a calculator will show that the square root of 30 is approximately 5.4772, which rounded to two decimal places is 5.48.
It's important to remember that while calculators do just what is asked of them, they do not account for significant figures or decimal places accuracy. Thus, when you use a calculator, you should adjust the final result accordingly to reflect the desired or required precision for the calculation in question.