Speed Maths 3

Yet another method to find Squares faster.
I will start with an example.
Say We need to find the square of 16.
The nearest 10 is 20.
To get 20, we add 4 to 16,
i.e 16+4=20
Since we have added 4, to get the nearest ten.
We subtract 4 from 16..
16-4=12
To get the square of 16, 20 * 12 + (4 ^ 2)
=240 + 16 = 256.
For a 2 digit number we go for the nearest 10.
If it is a 3 digit number we should go for the nearest 100.

Few more examples
1) 24
Nearest 10 is 20.
24- 4=20
So to get the square, 20 * 28 + (4 ^ 2 )
The answer is 576.

2) 111
Nearest 100 is 100
111-11 = 100
So to get the square 100 * 122 + (11^ 2)
=12200+121
=12321

Will post the next one on progressions.
But new concepts in progressions are limited.
So that will be a small post .

Speed Maths 2

Squares of Numbers from 70-130
Let the Number be X such that X is between 70 and 130.
Step 1: X-100.
Add this value to X.
The value will be the left most 2 or 3(As the case maybe) digits of the answer.
Step 2: Square (X-100)
This will be the right most 2 digits.
In case you get 3 digits, carry over to the left digit.

Example:
1) Number is 82.
82-100 = -18
82-18=64
Now 18 ^ 2 is 324.
3 will be carried over to 4 and that becomes 67.
Answer is 6724

2) 112
112-100 = 12
112 + 12 =124
124 will be the 3 left most digits.
12 ^ 2 is 144.
1 will be carried over to the 4 and
the Answer is 12544

Speed Maths 1

A small post.

For Finding squares of numbers between 30-70

Say the number is 'X' and X is between 30 and 70.

Step 1: Find x-25.
X-25 will be the first digit/first 2 digits of the required answer.
Step 2:Find (50-X)^2
This will be the right most 2 digits.In case the square is a 3 digit number,
carry it over .

Example: 43
43-25
=18
50-43
=7
7 ^ 2 = 49
43 ^ 2 is 1849

Example 2:35
35-25=10
50-35=15
15 ^ 2 =225
Answer: 10, from 225 25 will be the 2 right most digits and carry over 2 to the 0 on the left side
So it becomes 1225.

Answer: 1225