SQUARE AND CUBE ROOT OF ANY NUMBER

If you want to find the root value of number you have to know some values


NO         SQUARE                 CUBE

1                      1                              1

2                      4                               8

3                      9                               27

4                     16                              64
 
5                      25                             125

6                      36                              216
  
7                      49                              343

8                      64                              512

9                      81                              729

10                   100                             1000

Eg:

9409
Split the number after two digit from right
94 / 09 
09 the number ending in 9 from the above square table
The last digit of square root may be 3 / 7
Come to 94 from above square table it's above 9

SQUARE OF NUMBER END WITH 5: 

The number near by 94 ending with 5 is 95
Easy to find the square of the number ending 5,Split the number 9/5 .First take 9 multiply to 
The next number so 9*10 is 90 is the fist two digits of square.
The 5 in 95'S square is 25 this is the last 2 digit the square .The 95's Square is 9025.
The answer may be 93/ 97 we know 95's square is 9025 more the 93 so the answer is 97 

Eg 2:

784
7/84
84 ending with 4 so 2/8.
7 it is more then 2^2 bun not 3^2 it exceed the given value so 2.
Answer may be 22/28.22's near by value ending with 5 is 25,it's square is 2*3=6,5*5=25(625)
625<784 so not 22 the answer is 28.

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EASY TO REMEMBER THE SQUARES OF NUMBER 11 TO 30

1- 2469-four times(no of letters)-11 to 14
2-258-three times- 15 to 17
3-26-two times- 18 to 19
4-048-three times-20 to 22
5-27-two times-23 to 24
6-27-two times-25 to 26
7-28-two times-27 to 28
8-4-one time-29
9-0-one time-30

Now take square of 11- 1 (2) the second 1 in 11 square 1 so it is 121
Now take 12-1 (4) the second number 2 square 4 so 144
Now take 13  - 1 (6) the square of number 3 is 9 so 169
Its up to 14  we mention above 2469 for four times 11 to 14(2 for 11,4 for 12,6 for 13,...)

Take square of 15- 2 (2) square of 5 is 25 take last digit only so 225
Take square of 29- 8th row (4) first number 81 second number 9 square take last digit only so 841.

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CUBE OF ANY 2 DIGIT NUMBER

Cube of two digit number:

We already post the square based on same method the cube of 2 digit number.

Take the two digit number(BA)

Eg:
       (87):
A-7
B-8
                                                                         11
A^3                         7^3=                                 0343
A^2*B*3                 7^2*8*3=                   01176
A*B^2*3                 7*8^2*3=                 01344
B^3                          8^3=                          0512
--------------------------------------------------------------------
                                                                    0658503        
                                                              --------------------

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SQUARE OF ANY 2 / 3 DIGIT NUMBER

SQUARE:

Find the square of two digit number:

 (BA):

Eg: 

(29) Here 2 is B and 9 is A
                                                     1-remainder
A^2                  9^2=                    081
A*B*2              9*2*2=             036        (+)        [ A^2 +A*B*2  B^2] 
B^2                   2^2=                 04
----------------------------------------------------
                                                    0841
                                              ----------------
Find the square of three digit number:

(CBA):

Eg:

(193) Here 1 -C, 9-B, 3-A

A^2                          3^2=                            1  09             
A*B*2                      3*9*2=                     1054        (+)
B^2+(A*C)*2           9^2+(3*1)*2=         087
(B*C)*2                    (9*1)*2=                018
C^2                            1^2                          01
------------------------------------------------------------------------
                                                                   037249
                                                          --------------------------

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SIMPLIFICATION: Surds&indices

When simplification the question may follows the below formats so without wasting time extract the needed variable  apply values to the formula get a quick result.

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SIMPLIFICATION

VBODMAS Rule

SIMPLIFICATION-1(Round Off)

SIMPLIFICATION-2:Basics

SIMPLIFICATION: Surds&indices

SQUARE OF ANY 2 / 3 DIGIT NUMBER

CUBE OF ANY 2 DIGIT NUMBER

EASY TO REMEMBER THE SQUARES OF NUMBER 11 TO 30

SQUARE AND CUBE ROOT OF ANY NUMBER

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SIMPLIFICATION-2:Basics

When you find any fraction like this:

1 / 10,500 /10,1 / 1000,5689 / 1000
Dont waste your time just put dot from right to left based on the zeros in denominator.
1 / 10  :1 is numerator
           10 is denominator
Answers for above fraction is: 0.1, 50, 0.001, 5.689.

Convert decimal number into a fraction:

0.5555
here 5 repeats so the number 5/9 here the 9 is different types of number repeat.
 0.4545
here 4 and 5 repeats so 45/99 here 99 represents two different types of numbers repeating. 
0.5676767
Here 67 repeats so 567-5(the non repeating number) 562/990 two repeats but total three digits so add 0.

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VBODMAS Rule:

VBODMAS Rule:

V- vinculum or bar




                                                    
                                                   
                         B-Bracket and Order to Solve them










                                                                     

O-Of  

     D-Division

M-Multiplication 








A-Addition

S-Subtraction

Exanple:  {5-[6+(10-8)]}

i: (10-8)=2

ii: {5-[6+2]}

 iii: {5-8}

                               ANS:-3

                                                      

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SIMPLIFICATION-1(Round Off)

4.5 * 9582 / 6 = ?

1)7186.5
2)6126.15
3)8524.5
4)6357.5
5)None Of These

Solution:

Take 4.5 as 5-round it off
Take 9582 as 10(round of 9.582)-round it off
5 * 10 / 6 = 50 / 6 =8.3
we round of all the values more so the answer is less then we got
less the 8.3 near by value is 7186.5
this is the answer .

16.87+?-45.39=56.66

1)28.14
2)39.79
3)118.92
4) 85.18
5)None Of These

Solution:

Take 16.87 as 17-almost near
Take 45.39 as 45-round it off
Take 56.66 as 57-almost near
17-57-45=-?
17-102=-?
-85=-?
85=?
we round off to near by so the answer is also near by 85 is 85.18

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