Irrational Numbers and Their Operations

Math ⇒ Number and Operations

Irrational Numbers and Their Operations starts at 8 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Irrational Numbers and Their Operations. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

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?

If x = √2 and y = √8, what is x/y?

If x = √2 and y = 1/√2, what is x × y?

If x = √5 and y = 2, what is x + y? Is the result rational or irrational?

Is the product of two irrational numbers always irrational? Give an example to support your answer.

Prove that √3 is an irrational number.