Lets 'ab' is a 2 digit numbers.
Step2: now next 3 parts will be 54, 108, 216 (just created GP of the 4 terms, here first term is 27 & common ratio is calculated by unit's digit of the number with its 10th digit 6/3 => 2, so nxt three terms are find out by multiply by 2, here 54(27*2), 108(54*2) & 216(108*2) OR you may also find nxt 3 parts by 27*6/3=> 54, 54*6/3=>108, 108*6/3=> 216 In case GP ratio comes in Decimals)
_________________________________________________
300------7--------------------6------------------3
So cube of 67 is 300763
How to Find the Approximation Square root upto 2 decimal of any number??lets Find Square root of 10.
Step1: Find a integer whose Square is near 10, In this case its 3 whose square is 9
Step2: Subtract the square of 3 i.e is 9 from the number 10-9=> 1 Or find the remaining number
Step3: Divide the resulting number from step2 by twice of 3, In this case 1/3*2 => 1/6
So Square root of 10 is 3 + 1/6 => 3.16 approx.
lets find the square root of 90
Step1: 9(square of 9 is 81)
step2: (90-81) 9
step3: 9/9*2 => 1/2 or 0.5
So square root of root 50 is 9+0.5 => 9.5
Multiply any 2 digit number??? let ab*xy
a---b
x---y
____
Step1;Unit Digit will be y*b
Step2:10th Digit will be a*y+b*x (carry any to step 3)
Step3: Remaining Digits will be a*x+ if any carry from step2
Eg. Multiply 78*83
7---8
8---3
Step1: 4(4 will be Unit Digit & 2 carry)
Step2: (7*3+8*8) + 2 => 7( 7 will be 10th Digit & 8 carry)
step3: (7*8)+8 => 64
so 78*83 will be 6474
Another example. 152*63
Note; consider 15 as 1 digit or 'a' 2 as 'b', 8 as 'x' & 3 as 'y'
15---2
6---3
______
Unit Digit: 6
10th Digit: 7(5 carry)
Remaining Digits: 15*6+5=> 95
so it will be 9576
How to multiply a 3 digit number?? let abc*xyza----b----c
x----y----z
=======
Unit Digit will be c*z
10th Digit will be b*z+c*y+ if any carry from last step
100th Digit will be a*z+x*c+b*y+ if any carry from last step
1000th Digit will be a*y+ b*x+ if any carry from last step
Remaining Digits will be a*x+ any carry from last step.
As all knows still; a.Square of a number Ending with 5
75=>
Step1: Square of Unit Digit i.e. 25
step2: 8(7+1)*7
5625
b. Square of a number who is near 100 by taking base 100
Square of 98, 98-2/2^2 => 9604
Square of 96, 96-4/4^2=> 9216
Square of 102, 102+2/2^2=> 10404
Square of 108, 108+8/8^2=> 11664
Same method for finding a number near 10 by taking base 10
Square of 12, 12+2/2^2 => 144
Square of 14. 14+4/4^2=> 196
c. Multiply of 2 digit number whose 10th Digit is same & the sum of unit digit is 10
Lets take 34*36
Last 2 digits will be 4*6
first 2 digits will be 4*3(just add 1 to the 10th digit)
68*62
Last 2 Digits 16(8*2)
First 2 digits 7*6
4216
Some Square tips:
A perfect square ends in 0,1,4,5,6,8,9.
A number is not perfect square if it ends in 2,3,7 or 8.
If the number ends with 6, then its second last digit should be odd.
If the number does not end with 6, then its second last digit should be even.
If the number is even, its last two digits should be divided by 4.
So, if a number is not according to the above conditions, then the number is not a perfect square
@gotchapagal @vini2308 @NehaN03 @krishna_17 @sneh21 @sabrinakhan @nikskrish @chintu61 @koool.Miike @bankingaspirant @sbaaz @Pushpak1987 @adamsjimmy971 @ank_mission_IIM @namrata124 @fluffy @nav_2610 @Gato @Dev_MBApagal @UthnkUknwME @amarsaur @Santiago_2k13 & Others. Pls Forgive me(pls pity on poor soul. As tagging on a long post is a Herculean task as at every tag, pages automatically scroll up :sneaky:), Its 4:30 am in the morning & I feel dizzy now. There is no activity in past 2 hours on PG 
(I spent nearly 1 & 30 mins to create this post :|)
I wanna to add some more shortcuts, but now i can barely open my eyes. I m Done for the day. These days, I hardly come on PG, So Good Luck for First day & first show candidates.
PS: Don't attempt Shortcuts on exams if you have't enough practice of it. Otherwise you may botch up Calculation, Time & exam.
Thanks for reading!!
