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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
mathsComplex NumbersIntroduction to Complex Numbers

### Irrational Number Notation

This page reviews the representation of irrational numbers. The complex number notation is very similar to the representation of irrational numbers -- both are given as numerical expressions.

click on the content to continue..

Irrational numbers are 'numbers that cannot be represented as p/q and are on the number line.
The equation x^2 = 2 has the solutions in irrational numbers. Which one in the following is the exact solution?

• +-1.4
• +-1.41
• +-1.414
• none of the above is the exact solution
• none of the above is the exact solution

The answer is 'None of these is the exact solution'.

What is the value of x in x^2=2?

• +-sqrt(2)
• the solution is given as a numerical expression
• both the above
• both the above

The answer is 'Both the above'. sqrt(2) is a numerical expression involving a square root symbol.

What is the solution to (x-1)^2=2?

• +-sqrt(2)+1
• the solution is given as a numerical expression
• both the above
• both the above

The answer is 'Both the above'. sqrt(2)+1 is a numerical expression involving a square root symbol and an addition.

What is the ratio of circumference to diameter of a circle? Find the exact value in the following.

• 22/7
• 3.14
• pi
• pi

The answer is 'pi'. The number is represented with a symbol or a letter.

is pi a rational number?

• No, pi is an irrational number
• No, pi is an irrational number
• yes, pi is a rational number

The answer is 'No, pi is an irrational number'. This particular irrational number is represented with a letter pi.

Irrational numbers are represented as numerical expressions or with a symbol.

Representation of Irrational Numbers : Irrational numbers are represented with numerical expressions (eg: root(3)(4)+3) or with symbols (eg: pi, e)

Solved Exercise Problem:

Is e (a constant, that is base of natural logarithm) a rational number?

• No. e is an irrational number
• No. e is an irrational number
• Yes. e is a rational number

The answer is 'No. e is an irrational number'

slide-show version coming soon