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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.continue
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.



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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'

                            
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