MATHS SHORTCUTS
 

SQUARE AND SQUARE ROOT

 

Finding SQUARES & SQUARE ROOTS quickly in exam in necessary.

All you need is first to understand what is squares. 

WHAT IS SQUARE? 

It is the product of some number with itself. x square is x*x
For example,
9 is a 
square of 3
, since it can be written as 3 × 3.
To find square of a number, first learn squares from 1 to 30




SQUARE OF NUMBERS ENDING IN 5​


Say 25,
Take the first number which is 2 & increase it by 1 (2+1) is 3.                                  
Multiply these two numbers, 2 x 3 = 6.
Now just add 25 at the end, 6'25'.
So, 25 x 25 is 625.

One more example, 
Say 75
first number is 7, increase by 1, so 8.
7 x 8 = 56, add 25 at end.
So, 75 x 75 is 5625.
 
​Try 65, 125, .......

SQUARE OF ANY NUMBER 


Say 22,
So write 22 as (22 - 2) & (22 + 2), 
which is now easy 20 x 24 = 480.
Then take last number which is 2.
Square it which is 4 and just add it to the number.
So 480 + 4 = 484.

​One more example, 
Say 32,
So write 32 as (32 - 2) & (32 + 2), 
which is now easy 30 x 34 = 1020.
Then take last number which is 2.
Square it which is 4 and just add it to the number.
So 1020 + 4 = 1024.  

SQUARE ROOT OF A NUMBER 
To find square root of a number, one should be familiar with squares of 1 to 10.
If the given number ends in 1, then square root will end in 1 or 9
If the given number ends in 4, then square root will end in 2 or 8

​If the given number ends in 9, then square root will end in 3 or 7
If the given number ends in 6, then square root will end in 4 or 6 



EXAMPLE 1:

Say, Square root of 1024,
This number ends in 4, so last number should either 2 or 8.
Split the number as 10 / 24.
Then,
Take the first split, which is 10, So 10 lies between square of 3 & 4.
i.e.  9 < 10 < 16, So the first number is 3. 
3 ?  = 1024, the last number can be 2 or 8 as discussed.
Take the first number which is 3, increase it by 1 i.e 3+1 =4.
So, 3 x 4 =12.
Check if the first number is lesser or greater than 12,
If the first split is greater than 12 then it is 8 & if lesser than 12 then it is 2.
In our case it is 10 which is lesser, so the last number is 2.
3 2 is square root of 1024.
One more example,


EXAMPLE 2:

Say, Square root of 9409,

This number ends in 9, so last number should either 3 or 7.
Split the number as 94 / 09.
Then,
Take the first split, which is 94, So 94 lies between square of 9 & 10.
i.e.  81 < 94 < 100, So the first number is 9. 
9 ?  = 9409, the last number can be 3 or 7 as discussed.
Take the first number which is 9, increase it by 1 i.e 9+1 =10.
So, 9 x 10 =90.
Check if the first split number is lesser or greater than 90,
If the first split is greater than 90 then it is 7 & if lesser than 90 then it is 3.
In our case it is 94 which is greater, so the last number is 7.
9 7 is square root of 9409.

Try to find square root of these, 7569, 5041,......

PRACTICE, PRACTICE AND PRACTICE A LOT

@@@@ HAPPY LEARNING, DO MATHS QUICKER @@@@ 

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