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 10

If a = √7 and b = -√7, 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 = √3 and y = √12, what is x × y?

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

Is the number √18 rational or irrational?

Is the number √2/2 rational or irrational?

Is the number √49 rational or irrational?

Is the number 0.101001000100001... rational or irrational?

Is the square root of 49 rational or irrational?

Is π (pi) a rational or irrational number?

Given that √2 is irrational, prove that 5 + 3√2 is also irrational.

If x = √2 and y = √8, what is the value of (x + y)²? Is the result rational or irrational?

If x = √3 and y = 2√3, what is the value of x × y? Is the result rational or irrational?

Let a = √5 and b = 2 - √5. Is the sum a + b rational or irrational? Justify your answer.

Prove that the sum of a rational number and an irrational number is always irrational.