Irrational Numbers and Their Operations
Math ⇒ Number and Operations
Irrational Numbers and Their Operations starts at 8 and continues till grade 12.
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See sample questions for grade 12
Explain why the decimal 0.123456789101112... (where the digits are written in order) is irrational.
Explain why the sum of √2 and -√2 is rational.
Explain why π (pi) is considered an irrational number.
If a = √2 and b = -√2, what is a + b? Is the result rational or irrational?
If x = √2 and y = √3, what is x × y in simplest radical form?
If x = √2 and y = √8, what is x × y? Is the result rational or irrational?
Explain why the decimal 0.123456789101112... (where the digits are written in order) is irrational.
Is the number 0.101001000100001... (where the number of zeros between ones increases by one each time) rational or irrational?
Which of the following expressions is irrational?
(1) √49
(2) √2 + √3
(3) 2/3
(4) 0.5
Which of the following is a property of irrational numbers?
(1) They can be written as a ratio of two integers.
(2) Their decimal expansion is non-terminating and non-repeating.
(3) They are always negative.
(4) They are always greater than 1.
Which of the following is an example of an irrational number?
(1) 1.41421356...
(2) 1.5
(3) 3/7
(4) 0.333...
Which of the following is irrational?
(1) √16
(2) 0.75
(3) √7
(4) 1.25
Fill in the blank: The decimal expansion of an irrational number is ________ and non-repeating.
Fill in the blank: The number e (Euler's number) is an example of an ________ number.
Fill in the blank: The set of irrational numbers is ________ under addition.
Fill in the blank: The set of irrational numbers is ________ under multiplication.
Is the number √(2/3) rational or irrational?
Is the number √(7/49) rational or irrational?
Is the number 0.101001000100001... (where the number of zeros between ones increases by one each time) rational or irrational?
True or False: Every non-repeating, non-terminating decimal is irrational.
