Question

Which of these numbers is irrational? O A. - 5 9 O B. 1.618 C. 43 O D. VO​

Answer 1

D)
`√(6)`

Irrational numbers are numbers that cannot be expressed in the form of p/q where q is not equal to zero.

Here is how to understand if a number irrational or not:

• Irrational numbers will have decimal expansions which are non-terminating and non-recurring (no pattern or repetition o certain groups of numbers couldn't be observed and the decimal expansion will not ever end)

EXAMPLE: For non-recurring and non- terminating decimal expansions.

1. 2.258755655554517144516517849616128478462131...................
2. 76.2879485165886225568656559781230414746108....................
3. 4987.251484561515484513184964989494555121266....................

• In the above examples, it can be observed that all the decimal digits had no pattern and they will never end.

In this question, the answer is root 6. but it is not necessary that we have to find the decimal expansion, but we ccanfind it easily just by findinf if the given number is a perfect square or not.

EXAMPLE:

1. 
   `√(4)` is a rational number as 4 is a perfect square.
2. 
   `√(100)` is a rational number as 100 is a perfect square.
3. 
   `√(8)` is not a rational number as 8 is not a perfect square