Squares of Numbers from 1 to 50
1^{2} = 1 
= 4 
= 9 
= 16 
= 25 
= 36 
= 49 
= 64 
= 81 
= 100 
= 121 
= 144 
= 169 
= 196 
= 225 
= 256 
= 289 
= 324 
= 361 
= 400 
= 441 
= 484 
= 529 
= 576 
= 625 
= 676 
= 729 
= 784 
= 841 
= 900 
= 961 
= 1024 
= 1089 
= 1156 
= 1225 
= 1296 
= 1369 
= 1444 
= 1521 
= 1600 
= 1681 
= 1764 
= 1849 
= 1936 
= 2025 
= 2116 
= 2209 
= 2304 
= 2401 
= 2500 
Cubes of Numbers From 1 to 30
= 1 
= 8 
= 27 
= 64 
= 125 
= 216 
= 343 
= 512 
= 729 
= 1000 
= 1331 
= 1728 
= 2197 
= 2744 
= 3375 
= 4096 
= 4913 
= 5832 
= 6859 
= 8000 
= 9261 
= 10648 
= 12167 
= 13824 
= 15625 
= 17576 
= 19683 
= 21952 
= 24389 
= 27000 
Square Roots & Cube Roots
Last Digit of Any Number

Last digit of its Square

Last Digit of its Cube

1

1

1

2

4

8

3

9

7

4

6

4

5

5

5

6

6

6

7

9

3

8

4

2

9

1

9

0

0

0

Finding five digits Cube and Cube root tricks
You just need to remember 1 to 10 cubes and this is so easy for any one.
Finding six digits Cube and Cube root tricks
You just need to remember 1 to 10 cubes and this is so easy for any one.
Step 2: Take the number whose cube is nearest to 3869. That is 3869 is nearest to 15^{3} and 16^{3}. We take smaller one cube digit that is 15.
So the answer is 157.
Step 2: Take the number whose cube is nearest to 1728. That is 1728 is nearest to 12^{3} and 13^{3}. We take smaller one cube digit that is 12.
So the answer is 120.
Note: This technique is valid for exact cubes only. This is also a good method of finding approximations.
Procedure of finding the Square Root (Perfect Squares only)
 First find the last digit of the Square Root, which can directly be obtained by looking the last digit of the Number and then refer to the above table which can be used for finding the last digit of the square root
 Next, ignore the last 2 digits of the number and look at the numbers which remain. Think of a number, whose square is just equal or less then this remaining number.
Find square root of 4096
 From the above table, we get last digit of the square root as 6
 Then we ignore 96 and focus on 40. From this we get the number 6, whose square is just lesser than 40
 Hence the square root is 64
Constant Product Rule (1/x) & 1/(x+1)
A 1/x increase in one of the parameters will result in a 1/(x+1) decrease in the other parameter if the parameters are inversely proportional.
 A lady travels from her home to office at 4km/hr and reaches her office 20 min late. If the speed had been 6 km/hr she would have reached 10 min early. Find the distance from her home to office?
 A 20% increase in price of rice. Find the % decrease in consumption a family should adopt so that the expenditure remains constant.