Learn to Find Square of Recurring Number

Finding Square of a number between 200 and 300
We have already seen different Vedic math tips and tricks to find square of a number in the post

Square of a number – Part 1    and in the post

Square Of a Number Between 100 and 200
Now let us find square of number between 200 and 300.

Square of any number between 200 and 300 will always be five digits.

Step1: Last two digits of the square are the square of the last two digits.
            Take other digits as carry.

Step2: Next two digits of the square are four times the last
            two digits plus carry from Step1

Step3: Initially take first digit of the square as 4 i.e. 2²= 4
            and add any carry which comes from Step2.

Step4: Answer= Step3| Step2| Step1

Let us take an example 215²=?

Step1: Square of last two digits= 15²= 225, last two digits= 25 carry 2

Step2: Four times last two digits= 4× 15=60, next two digits= 60+ 2= 62

Step3: First digit= 4 +any carry from Step2= 4+ 0= 4

Step4: Answer= 46225

Let us take one more example 267² =?

Step1: Square of last two digits= 67²= (60+ 7)²= 60²+ 2× 60× 7+ 7²
                = 3600+ 840+ 49= 4489, Last two digits= 89 carry= 44

Step2: Four times last two digits+ carry= 4× 67+ 44= 268+ 44=3 12
            Next two digits= 12 carry= 3

Step3: 4+ carry= 4+ 3=7

Step4: Answer= 71289

Practice:

1) 234²
2) 265²
3) 289²
4) 277²
5) 253²
6) 205²
7) 219²
8)234²

Square of Recurring Number

What is recurring number?

Number series which repeats itself to form a number is a recurring number. e.g. 44444, 121212, 123123, 55555

How to find square of these numbers?

Let us take number m recurring n times, let us take n=5.

Find ( mmmmm)²= ?

Step1: First find how many times (n), number m is repeating, in this example n= 5

Step2: Find square of m = m² 

Step3: Write table of m² till n. i.e. m²| 2× m²| 3× m²| 4× m²| 5× m²

Step4: Now write ahead of Step3 table in the reverse direction till m² is reached
            m²| 2× m²| 3× m²| 4× m²| 5× m²| 4× m²| 3× m²| 2× m²| m²

Step5: To get answer start from right side, just keep units digit from each number
            and pass the balance digits as carry across the vertical line.

Let us take example to explain the steps taken to find square of the recurring   numbers.

Example1 (44444)² =?

Step1: 4 is repeating 5 times

Step2: find square of 4= 4²= 16

Step3: Write table of 16 till 5 times as n=5,
            16| 32| 48| 64| 80

Step4: Now write table in reverse direction till we reach 16 .
            16| 32| 48| 64| 80| 64| 48| 32| 16

Step4: To get answer start from right, keep units digit.

16= 6, carry 1

32+ 1= 33= 3, carry 3

48+ 3= 51= 1, carry 5

64+ 5= 69= 9, carry 6

80+ 6= 86= 6, carry 8

64+8= 72= 2, carry 7

48+7= 55= 5, carry 9

32+5= 37= 7, carry 3

16+ 3= 19 =19

Write answer from bottom to top

Ans. = 1975269136

Isn’t it cool? This is how we can use Vedic math to make math easy.

Practice:

1) (55555)²
2) (1212)² tip: take 12 as recurring number.
3) (333)²
4) (666)²
5) (1313)²