Which of the following is an irrational number? *
1 point
a. √16
b. √(12/3)
c. √12
d. √100
Answers
Step-by-step explanation:
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√12 is an irrational number.
Option (c) is correct.
Given:
To find:
- Which of the above written numbers is an irrational number?
Solution:
Definition to be used:
- An irrational number can not be expressed as p/q form, where p and q are integers and q≠0.
- A rational number can be expressed as p/q form, where p and q are integers and q≠0.
Step 1:
Check for option a:
we know that
and
or
Thus,
Option a) is rational number.
Step 2:
Check for option b:
Rewrite the number, as shown below
or
Thus,
Option (b) is a rational number.
Step 3:
Check for option c:
it can be written as
or
or
As √3 is not integer. So, while writing it as
it is still an irrational number.
Thus,
Option (c) is irrational.
Step 4:
Check for option d:
It may be written as
or
or
Thus,
Option (d) is rational number.
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