Real Number System

Math ⇒ Number and Operations

Real Number System 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 Real Number System. 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 sum of two rational numbers is always rational.

Express √50 in simplest radical form.

Express 0.272727... as a fraction in simplest form.

If a real number x satisfies x² = 9, what are the possible values of x?

If x = √3 and y = √12, what is x × y?

If x = 2 + √3 and y = 2 - √3, what is the value of x × y?

If x = 2 + √5, find the value of (x - 2)².

If x = 3 + √7, what is the conjugate of x?

Prove that √2 is an irrational number.

Consider the set S = {x ∈ ℝ : x² < 0}. What is S?

Given that x is a real number such that x³ = 8, what is the value of x?

If x = 2 + √5 and y = 2 - √5, what is the value of x² + y²?

Let x = √2 + √3. Without using a calculator, determine whether x is rational or irrational. Justify your answer.

Let x = √2 and y = √8. Express x + y in simplest radical form.

Prove that if r is a nonzero rational number and s is an irrational number, then r + s is irrational.