<h2>
Answer:</h2>
<u>Ques 1)</u>
B)
<u>Ques 2)</u>
D)
<h2>
Step-by-step explanation:</h2>
We know that an irrational number is a number which could not be expressed in the form of p/q where p belongs to integers and q belongs to natural numbers.
Also the decimal expansion of an irrational number is:Non-terminating and non-repeating.
( whereas the number is a rational number if it could be expressed in the form of p/q where p is a integer and q is a rational number.
Also, the decimal expansion of a number is terminating and repeating )
<u>Ques 1)</u>
A)
We know that this number could also be represented by:
i.e. the number is a rational number since, it is represented in the form of p/q where p= -4 and q=1
B)
On further simplifying
Hence, the number could not be expressed in the form of p/q
Hence, it is a irrational number.
C)
It could be represented as:
i.e. it is a rational number.
Since p= 2 and q=1
D)
We know that this number could also be represented by:
i.e. the number is a rational number since, it is represented in the form of p/q where p= 4 and q=1
Hence, the correct answer is: Option: B
B)
<u>Ques 2)</u>
A)
Since, the decimal expansion is a repeating decimal since there is a bar over 8.
Hence, the number is a rational number.
B)
It could also be written as:
Since, the number is in the form of p/q where p=5 and q=1
Hence, the number is a rational number.
C)
The decimal expansion is terminating.
Hence, the number is a rational number.
D)
It could also be written by:
Since, the number does satisfy the definition of irrational number i.e. it could not be represented in the form of p/q where p is a integer and q is a natural number.
Hence, we get:
The number is a irrational number.