Sunday, 21 April 2013

Power of 1/3

Power of 1/3 :
This is the cubes table

Table : 1
Number Cube
1     1
2      8 
3    27
4    64
5   125
6   216
7   343
8   512
9   729
10  1000


This table formed by using Underlined Digits
Table : 2
Number Cube ends with
1 1
2 8
3 7
4 4
5 5
6 6
7 3
8 2
9 9
10 0

Solving cubes little bit tricky but we can do it using a simple table it using a simple table
you have to remember this table-2
when you see 1 it's 1, 2 it's 8, 3 it's 7..........,the cube of the number ends in this formatHow ? we can do for more digits
Step 1:
 Divide first three digits
 for example if the number is 103829 it should be 103 | 829
another example :
if the number is 39304 it should be 39 | 304

Step 2:
We have to solve the right part first then shift to the left part of the number .
Example : 287496 cube ?
Step 1:  287496 >>>>>>> 287|496
Step 2: The number ends with 6 so ...the cube of the number ends with 6 (From table -2) _______________6

Step 3:  Now consider 287 it is lies between cube of 6 and 7 (From table -1) ______________66
    >>>>>  
so next value is 6
Step 4: the answer is 66
Another Example :

Saturday, 13 April 2013

How to find Square Root of a number

Finding root of a number
To find Root of a number we have to follow some basic rules.
The first and last rule is just a square table
(In this scenario we do some comparisons with known values)
Te table values :
Number Square
1 1
2 4
3 9
4 16
5 25
6 36
7 49
8 64
9 81
10 100

By observing the above table we can conclude that (by comparing both first digits of numbers )
Square first digit Number
1 1 or 9
  4  2 or 8
9 3 or 7
6 4 or 6
5 5
0 0

By using following table-2
if the number first digit is 9 then The root of that number  first digit is   3 or 7
if the number first digit is 6 then The root of that number  first digit is  4 or 6
Note: By observing first table square column we can conclude that square root of any number doesnot ends with 2 ,3,7 or 8

To find Square roots of unknown numbers we have to use some simple known values.
At last we reached the end to find square roots of a number just follow the TABLE-2 AND TABLE-3
Number Square
10 100
20 400
30 900
40 1600
50 2500
60 3600
70 4900
80 6400
90 8100
100 10000
Example :
Find square root of  7744 ?
Solution :
Step 1 : 7744 first digit is 4 so the square root  first digit is 2 or 8.
Step 2 : compare this number with second table. The value is in between 80 and 90 so that the number may be 81,82,83,84,85,86,87,88,89.

Step 3 : By using Step 1 we can conclude that the number First digit is 2 or 8 so The Number is either 82 or 88.
Step 4 : If 7744 is close to 6400 then answer will be 82.
Step 5 : If 7744 is close to 8100 then then answer will be 88.