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Lesson Topics Discussion Quiz: Class Homework

Example1

Title: Classifying Numbers

Grade 6+ Lesson s1-l1

Explanation: The best way to understand algebra is by looking at some examples. Take turns and read each example for easy understanding.

Examples

Topics → Definition Example1 Example2 Example3

Identify the classification(s) for the number \$\sqrt3\$.

Step 1

The given number is \$\sqrt3\$.

Explanation:

Here we write the given data.

Step 2

Real numbers include all rational and irrational numbers. Since \$\sqrt(3)\$ is a non-negative, non-repeating, non-terminating decimal, it is a real number.

Explanation:

Determining whether a given value is a real number or not.

Step 3

Assume \$\sqrt(3) \$ is rational.
Square both sides of \$\sqrt(3) = p/q \$ to obtain 3 = \$(p^2)/(q^2)\$.
Deduce that p and q must both be divisible by 3, leading to a contradiction.

Explanation:

Verifying it as an irrational number. Therefore, \$ \sqrt(3) \$ is both a real number and an irrational number.