Mathematics
Grade-8
Easy
Question
Which number is irrational?
- -0.9
- Square root of 3
Hint:
Terminate decimal refers to a decimal with a finite number of digits after the decimal point.
A recurring decimal refers to a decimal with a repeated digit or digits at the end after the decimal point.
Rational numbers refer to those numbers that can be represented as a simple fraction and can be either a whole number, a terminating decimal or a non terminating recurring decimal.
Irrational numbers refer to those numbers that cannot be represented as a simple fraction and are non-terminating non-recurring decimal.
The correct answer is: Square root of 3
TO FIND-
Irrational number from the given options.
SOLUTION-
From the given options, to find the irrational number, we find the option that is a non-terminating, non-recurring decimal.
a. -0.9
The given number is a non-terminating decimal.
Hence, option a is a rational number.
b. √3 = 1.732............
Using Long division method, we find the square root of 3. (Refer image attached below).
The given number is a non-terminating, non-recurring decimal.
Hence, option b is an irrational number.
c. 9/500 = 0.018
The given number is a terminating decimal.
Hence, option c is a rational number.
d. 7/9 = 0.77777777.......
The given number is a non-terminating, recurring decimal.
Hence, option d is a rational number.
FINAL ANSWER-
Option 'b' i.e. '√3' is the correct answer to the given question.
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