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 8

If a = √3 and b = 2, what is a × b?

If x = √2 and y = √2, what is x × y?

If x = √2 and y = √3, what is x × y?

If x = √2 and y = √8, what is x × y?

If x = √2, what is 2x?

If x = √2, what is x²?

If x = √5 and y = 3, what is x + y?

Is the number √2 + √3 rational or irrational?

Is the number √49 rational or irrational?

Is the number 0.101001000100001... (where the number of zeros between ones increases by one each time) rational or irrational?

Is the number 0.123456789101112... (where the digits are written in order) rational or irrational?

Is the number 2 + √3 rational or irrational?

Is the number π (pi) rational or irrational?

Consider the number 0.101001000100001... where the number of zeros between ones increases by one each time. Is this number rational or irrational? Explain your answer.

If a = √5 and b = 2, what is the value of (a + b) × (a - b)?

If x = √7 and y = √7, what is the value of x × y? Is the result rational or irrational?

Prove that √11 is an irrational number.