Question

Select all the true statements.

You can compare irrational numbers using rational approximation.

Square roots can be compared and ordered by comparing and ordering the numbers underneath the radical symbol.

You cannot compare the value of rational and irrational numbers.

The closer together the numbers being compared, the more decimal places you need to use.

All irrational numbers have some repeating pattern which can be used to compare them to rational numbers.

Answer 1

1,2,4

Explanation:

1) You can compare irrational numbers using rational approximation.

2) Square roots can be compared and ordered by comparing and ordering the numbers underneath the radical symbol.

4) The closer together the numbers being compared, the more decimal places you need to use.

Answer 2

The correct option are;

1) You can compare irrational numbers using rational approximations

2) Square roots can be compares and ordered by comparing and ordering the numbers underneath the radical symbol

3) The closer together the numbers being compared, the more decimal places you need to use

Explanation:

1) Two irrational numbers can be compared using rational approximation because both rational and irrational numbers are part of the real numbers and therefore have defined positions on the real number line such that the values of rational and irrational numbers can be compared based on their relative position on the number line.

2) The values of a square roots is directly proportional to the value under the radical symbol, therefore, square roots can be arranged in their order of magnitude and can also be compared by comparing and ordering the numbers under the radical symbol

3) When two numbers are very close, the difference between the numbers will be small. Therefore in order to clearly define the differences between two close numbers, the value of the difference between the numbers needs to be amplified by increasing the detail or the number of decimal place values of the numbers

Similarly, comparing two numbers that are very close requires increasing the detail or the number of decimal place values of the numbers