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 11

Explain why the sum of two irrational numbers can be rational, giving an example.

Express √50 in simplest radical form.

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

If a real number x satisfies x³ = 27, what is the value of x?

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

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

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

Prove that √3 is an irrational number.

Which property of real numbers is illustrated by the equation (a + b) + c = a + (b + c)?

Write the decimal expansion of 1/8.

Consider the decimal 0.12345678910111213... formed by writing the natural numbers in order after the decimal point. Is this number rational or irrational?

Given the equation x² - 5x + 6 = 0, determine whether the solutions are rational or irrational. Justify your answer.

If x is a real number such that x⁴ = 16, list all possible real values of x.

Let a = √7 and b = √11. Without calculating their exact values, determine whether a + b is rational or irrational. Explain your reasoning.

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

Let x = √2 and y = √8. Compute x × y and state whether the result is rational or irrational.

Prove that there is no rational number whose square is 12.