Mathematics
Grade-8
Easy

Question

Which number is irrational?

  1. -0.9
  2. 9 over 500
  3. 7 over 9
  4. Square root of 3

hintHint:

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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