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Squares of Numbers from 1 to 50

12 = 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.
 
Example
 = ?
Solution
Step 1: Last digit of cube number from right side is 4 that we consider 64 = 43 we put down 4. Step 2: Take the number whose cube is nearest to 13.
 
That is 13 is nearest to 23 and 33. We take smaller one cube digit that is 2.
 
So the answer is 24.
 
Example-2
 = ?
Solution
Step 1: Last digit of cube number from right side is 5 that we consider 125 = 53. We put down 5. Step 2: Take the number whose cube is nearest to 15. That is 15 is nearest to 23 and 33. We take smaller one cube digit that is 2.
 
So the answer is 25.

 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.
 
Example
 = ?
Solution
Step 1: Last digit of cube number from right side is 5 that we consider 125 = 53 we put down 5.
 
Step 2: Take the number whose cube is nearest to 166.That is 166 is nearest to 53 and 63. We take smaller one cube digit that is 5.
 
So the answer is 55.
 
Example
 = ?
Solution
Step 1: Last digit of cube number from right side is 3 that we consider 343 = 73. We put down 7.
 
Step 2: Take the number whose cube is nearest to 185. That is 185 is nearest to 53 and 63. We take smaller one cube digit that is 5.
 
So the answer is 57.
 

You just need to remember 1 to 10 cubes and this is so easy for any one.

 

Example
 = ?
Solution
Step 1: Last digit of cube number from right side is 3 that we consider 343 = 73 we put down 7.

Step 2: Take the number whose cube is nearest to 3869. That is 3869 is nearest to 153 and 163. We take smaller one cube digit that is 15.

So the answer is 157.
 

 

Example
 = ?
Solution
Step 1: Last digit of cube number from right side is 0 that we consider 1000 = 103 we put down 0.

Step 2: Take the number whose cube is nearest to 1728. That is 1728 is nearest to 123 and 133. 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)

  1. 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
  2. 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.
Example

Find square root of 4096

  1. From the above table, we get last digit of the square root as 6
  2. Then we ignore 96 and focus on 40. From this we get the number 6, whose square is just lesser than 40
  3. Hence the square root is 64

Constant Product Rule (1/x) & 1/(x+1)

This rule can be applied when we have two parameters whose product is constant, or in other words, when they are inversely proportional to each other.
 
eg) Time × Speed = Distance, Price × consumption = Expenditure and Length × breadth = Area

 

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.

 
Lets see the application with the following examples
  1. 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?
     
    Solution: Assume original speed = 4km/hr. Percentage increase in speed from 4 to 6 = 50% or ½. 1/2 increase in speed will result in 1/3 decrease in original time = 30 minutes.(from given data). Original time = 90 minutes = 1.5 hours.
     
    Answer = 4 × 1.5 = 6 km
  2. A 20% increase in price of rice. Find the % decrease in consumption a family should adopt so that the expenditure remains constant.
     
    Solution: Here price × consumption = expenditure (constant). Using the technique, 20% (1/5) increase results in 16.66% (1/6) decrease in consumption.
     
    Answer = 16.66%




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