Shortcut formule on number system

Important shortcut formula on number system :

1.  To find the larger between ³√3 and ⁴√5

Solution: 
 Take lcm of surds which are 3 and 4 here .
Lcm of 3 and 4 is 12 
Convert each surd into surd of 12.
³√3=¹²√3⁴=¹²√81
⁴√5=¹²√5³=¹²√125

Clearly ¹²√125 >¹²√81 
So ⁴√5 is greater.



2. If  √x-√x-√x-.....upto infinity ( root is over whole equation).

then x=n(n+1)
value of expression is given by n.

if √x+√x+√x+.....upto infinity

then x=n(n+1)
value of expression is given by n+1.


3.  Find gretest between 1/2,2/3 ,3/4.
Solution.

By cross multiplying first two terms we will find the greatest between them.
1*3 and 2*2
3 and 4 .As the right hand side is geater so second number will be greater. 

By again crossmultiplying the greatest of two numbers and third number.
8 and 9 
Clearly third number is largest.

This method is best for findind the smallest and largest numbers. It will require some practice to solve the questions fastly by this method.

eg.  find largest 1/5,10/11,4/7,7/9
You can solve question in just 3 steps
->> 11 and 50 second is greater
->>  70 and 44 second is greater
->>  90 and 77 second is greater.


For finding lesser term just pick the side having smaller number.