Question

Which of the following is an irrational number

Answer 1

Answer:
`-√(14)` in the lower right corner

===========================================================

Step-by-step explanation:

A rational number is any fraction like 2/3 or 7/9. Pick any two integers, divide them, and you get a rational number. Zero cannot be in the denominator.

Based on that, we can see that 129/999 is rational, which is crossed off the list of potential answers.

Furthermore,
`√(16) = 4 = (4)/(1)` is also rational since we can form a fraction of integers. Cross this off the list as well. Always try to simplify the expression as much as possible.

-----------------

When converting a fraction to decimal form, it turns out that any rational number has either two cases:

• The decimal terminates or stops (eg: 1/2 = 0.5)
• The decimal pattern repeats forever (eg: 2/99 = 0.02020202...)

This means the number
`-7.\overline{34}` = -7.3434343434... is also rational, which is crossed off the list also.

----------------

The only thing left is
`-√(14)` which is not rational, and therefore we consider it irrational. We cannot form a fraction of integers to represent this square root value. Note how 14 is not a perfect square.

Answer 2

-7.34 repeating

Step-by-step explanation:

A rational number is described as a number that can be expressed as a fraction or ratio of two integers and -7.34 repeating is the only option that does not fit this description. Repeating decimals can not be rational.