Finding the cube roots

Finding Cube Roots requires some background

Background	Last digit
13 =	1	1
23 =	8	8
33 =	27	7
43 =	64	4
53 =	125	5
63 =	216	6
73 =	343	3
83 =	512	2
93 =	729	9

From the above illustration we can take out that last digit of 2³ is 8, 3³ is 7 and vice-versa. All other repeats itself.

Procedure of finding a cube: -

• Start from right and put a comma when three digits are over

Examples: -

9,261

1,728

32,768

175,616

• After putting the comma see the last digit of the number; compare that with table provided above. You get the last digit.
• Now see the first group of numbers and ascertain cube of which number is less than the group. That number is your first digit.
• You have thus found first digit and last digit.

Let us take an example: -

Steps: -

• Counting from last we put comma after 9.
• By seeing the last digit we ascertain that last digit of cube root will be 1.
• Now we see 9 and ascertain that 2³ = 8, is less than 9 and 3³ = 27 is more.
• Our first digit thus comes to 2, and the answer is 21.

Another Example: -

• By seeing last digit we find last digit of cube root is equal to 2.
• By seeing 32 we put 3, as our first digit as 3³ = 27 is less than 32 and 4³ = 64 is more.
• Our answer is 32.

Squaring the 2 digit number ending with 5

Let us start with an example: -

How would you multiply this in conventional way?

Let us solve it: -

What are the steps you took here?

• First you multiplied 65 by 5 and wrote it below the line (325)
• Then you multiplied 65 by 6 and wrote it below the first row leaving one space from right (390)
• You added the numbers in first row with the numbers in the second row by first putting right most digits down and adding other digits thereafter conventionally.
• You got 4225 as answer.

Now let us do it by magical method: -

  a5 x  a5 = a(a+1) | 25

 

What did we do here?

• We multiplied 5 by 5 and put 25 as right hand side of the answer.
• Multiple left digit…i.e. 6 with 6+1 …so we get 6 into 7…so 42

Did you get it?

Let us do some more by the method learned just now!

Magical Squaring Technique For Numbers 11 to 19

Let us first find square of 11 using the formula: -

The formula is self-explanatory. However, let me explain it for more clarification: -

• Slash used here is just a separator.
• Our operating zone is 10 x 1 or simply 10.
• 11 is one more than 10.
• We added 1 to 11 to make it 12.
• Number of digits after the slash can be only one.
• If the number of digits after the slash exceeds one then we place only the right most digit after the slash and the remaining digits gets added to left hand side of the slash.

Will you be able to find squares of other numbers in a similar manner? Try.

You can work like this up to 19^2. What about numbers above 20?

Formula remains same with a slight change. The change you will appreciate..

Vedic mathematics : Easy way of finding square of a number ending with 5

quick way to square numbers that end in 5 using the formula BY ONE MORE THAN THE ONE BEFORE.

• 75² = 5625 75² means 75 x 75.
  The answer is in two parts: 56 and 25.
  The last part is always 25.
  The first part is the first number, 7, multiplied by the number "one more", which is 8:
  so 7 x 8 = 56
• Similarly 85² = (8 * 9) 25 = 7225
  

Square of 2 digit number having same digit, AA

N     N^2
11   121
22   484
33   1089
44   1936
55   2916
66   4356
77   5776
88   7744
99   9801


Now suppose that number is AA
than AA = 10A+A
We know,
(a+b)^2 = a^2 + 2ab + b^2
AA ^ 2 = (10A +A) ^2 = 100*(A^2 ) + (A^2 ) + 2*10A*A= 121*(A^2 )
So all these numbers are divided by 121 :P

So if you want to find 99^2, you can do 121 * (9^2), though it may look tough this way.
=121 * 81
But for 22 ^2 = 121 * 4 = 484 , i.e. little easier