Answer:
1) True
2) True
3) False
4) True
Explanation:
1) You can compare irrational numbers using rational approximations
The above statement is true as given two irrational numbers which can be expressed in decimal format, by rounding up the numbers to a certain number of decimal places, the values of the irrational numbers will be different
2) Square roots can be compared and ordered by comparing and ordering the numbers underneath the radical symbol
The above statement is true as the the values of the numbers under the radical symbol are directly proportional to the square root
3) You cannot compare the value of rational and irrational numbers
The above statement is false because the value of an irrational number can be found between two rational numbers. Therefore, the value of an irrational number is higher than the rational number that precedes it on the left of a number line
4) The closer the numbers being compared, the more decimal places you need to use
The above statement is true as a higher level of detailed value of the numbers being compared will be required given the closeness in value of the numbers being compared.