Page 2 - Lesson Notes
P. 2
Example: Find an irrational number between and
Solution: 2 =1.414 3 =1.732
Therefore, an irrational number between them is 1.515115111...
Method 2 If and are two positive irrational numbers then is an
irrational number between them such that ab is not a prefect square.
Example : Find a irrational number between and
Solution : A we know that if and are two positive irrational numbers
then is an irrational number between them
Therefore 6 is the required number.
Representation of irrational numbers on a number line
Irrational numbers can be represented on a number line by two methods
a) Squareroot Spiral method
b) Tunnel method
Squareroot Spiral Method
On a Number line a perpendicular is drawn of 1 unit with base 1 unit i.e at a
distance of 1 unit (in the positive direction) from 0 marked on the number line.
The hypotenuse of this triangle is 2 units.et 6
The same steps re repeated with base 2 units and perpendicular 1 unit to
get 3 .Similarly,other irrational numbers are obtained.
.
Tunnel method/perpendicular type.
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