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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